Holography and Quantum Gravity

Can a quantum theory without gravity describe a higher-dimensional gravitational spacetime? Holography makes that question concrete through dualities such as AdS/CFT. Quantum gravity asks the broader question of how spacetime, matter, and their observables fit into a quantum description.

This volume develops holographic calculations, black-hole physics, and several approaches to quantum gravity. Its organizing distinction is between a specified duality, a controlled approximation within it, and a proposal for a more general theory. Learning to calculate a boundary correlator or a black-hole entropy includes learning which of those statements the calculation supports.

Where to begin

For a first holographic calculation, begin with claims and observables, then Chapters 2–3 for the bulk regime and dictionary. Follow Chapters 6–7 to compute a renormalized correlator; Chapter 8 connects it to bulk scattering and locality.
For black holes and information, begin with thermal phases after the dictionary in Chapter 3. Chapters 12–15 develop reconstruction and entropy; Chapters 17–21 supply laboratories, microscopic counts, path integrals, and information questions.
For a quantum-gravity proposal or possible observation, begin with claims and observables, then choose Chapters 25–29. Compare defined observables, controlled limits, and tests before drawing conclusions about a complete theory.

Helpful background. Large-N limits, conformal data, and sparse spectra prepare the bulk expansion. Duality dictionaries prepare comparisons. Review thermal states, regulated entropy, causal geometry, and gravitational approximation regimes as your route requires.

Chapters

Quantum-Gravity Claims, Observables, and Evidence — Specify what a proposed equivalence, calculation, or observation actually establishes.
Large N and Semiclassical Bulk Criteria — Determine which spectral and correlation properties support a weakly coupled, approximately local bulk.
AdS Geometry, Boundary Problems, and the Dictionary — Turn a bulk boundary-value problem into a precise map between fields, sources, and operators.
String, Brane, and Top-Down Constructions — Trace a gravitational description to branes, compactification, flux, and a controlled decoupling limit.
Nonperturbative String- and M-Theory Definition Proposals — Compare what matrix and string-field constructions define and what remains to establish.
Holographic Renormalization and Radial Dynamics — Extract finite responses, Ward identities, and anomalies from asymptotic boundary data.
Witten Diagrams and AdS Perturbation Theory — Compute boundary correlators from bulk contact and exchange processes, including corrections.
AdS Scattering, Mellin Methods, and Bulk Locality — Relate analytic boundary data to bulk interactions while controlling contact terms and limiting procedures.
Thermal Phases and AdS Black Holes — Compare gravitational saddles in a specified ensemble and test their thermodynamic stability.
Lorentzian, Nonequilibrium, and Chaotic Holography — Compute causal response and dynamical observables with the correct state and horizon prescription.
Holographic Matter, Transport, and Model Building — Use gravitational models to study mechanisms without assuming they identify a material’s microscopic theory.
Bulk Reconstruction and Gravitational Dressing — Represent bulk observables in boundary variables while respecting gravitational constraints.
Holographic Entropy and Quantum Extremal Geometry — Relate boundary entropy to bulk surfaces and quantum corrections within a stated approximation.
Modular Response, Relative Entropy, and Emergent-Gravity Claims — Determine which gravitational statements follow from information identities and which assumptions they require.
Entanglement Wedges and Holographic Quantum Error Correction — Describe regional reconstruction as a recovery problem with an explicit code subspace and accuracy.
Holographic Complexity Proposals and Diagnostics — Compare proposed geometric measures of complexity and the choices that make them inequivalent.
AdS3/CFT2 and Three-Dimensional Gravity — Use two-dimensional conformal structure to study three-dimensional gravity and black holes.
AdS2, JT Gravity, SYK, and Random Matrices — Explore near-AdS2 dynamics while distinguishing a fixed quantum system from an ensemble.
Black-Hole Microstates and Stringy Entropy — Compare microscopic counts, protected indices, and gravitational entropy in controlled settings.
Wormholes, Gravitational Path Integrals, and Ensembles — Specify the contour, topology sum, and averaging assumptions behind gravitational amplitudes.
Black-Hole Information, Islands, and Interiors — Distinguish entropy calculations and reconstructable regions from microscopic evaporation dynamics.
Higher-Spin and Vector-Model Holography — Study holographic regimes with higher-spin fields that need not resemble Einstein gravity.
de Sitter and Cosmological Holography — Identify the cosmological observables and assumptions entering proposed boundary descriptions.
Flat-Space, BMS, and Celestial Holography — Connect asymptotic symmetry, soft physics, and celestial transforms without assuming a complete dual theory.
Quantum-Gravity Consistency and Swampland — Separate conditional consistency results from conjectures and test their assumptions and counterexamples.
Canonical, Loop, Spin-Foam, and Group-Field Quantum Gravity — Follow quantized constraints and discrete structures toward physical observables and a semiclassical limit.
Asymptotic Safety, Causal, and Discrete Quantum-Gravity Programs — Assess fixed points and continuum limits using regulator, truncation, and refinement tests.
Quantum Cosmology and Singularity-Resolution Programs — State what a cosmological state, clock, or bounce calculation demonstrates about singularities.
Quantum-Gravity Phenomenology and Comparative Status — Connect proposed mechanisms to measurable signals, uncertainties, and alternative explanations.

How the ideas connect

Consider a scalar operator in a conformal field theory with a specified semiclassical AdS dual. Its source becomes boundary data for a bulk scalar. Solve the bulk boundary problem, renormalize the on-shell action, and vary the resulting generating functional to obtain correlators. Geometry, field normalization, boundary conditions, and the approximation order are all inputs. This source-based dictionary is developed in Witten 1998, § 2.3, preprint pp. 8–9 (PDF).

The example links the first computational chapters: large-N reasoning motivates a weak bulk expansion; the dictionary identifies the observable; holographic renormalization removes boundary divergences; Witten diagrams organize interactions. A matching two-point function alone does not establish an interacting local bulk. The additional role of spectral and correlation data is discussed in Harlow 2018, §§ 2.3–2.4 and 3.2.

Changing the question changes the calculation. Thermal response needs a state, ensemble, and causal prescription. Regional reconstruction needs an accessible algebra and an approximation domain. An entropy result needs a region and a prescription for quantum corrections. The familiar smooth, weakly curved bulk is one regime of holography; it is not implied by large N alone, and higher-spin models teach different lessons.

The comparison of quantum-gravity claims connects a proposed statement to its observable, dictionary, approximation, and tests. For a holographic model, ask what would change if a neglected correction became large. For a quantum-gravity program, ask how physical observables and a semiclassical limit are recovered. For phenomenology, ask whether alternative mechanisms produce the same signal. A successful model calculation answers its stated question; further conclusions require further evidence.

Compare assumptions, tests, and limitations across all 29 chapters

Theories, observables, and domains of validity

This detailed comparison preserves the conditions behind each route. Its literature assessments are dated 10 August 2026; current developments belong in the research field. The table is supplementary to the chapter guide and scientific explanation above.

Scroll horizontally to compare all columns. Use the Left and Right arrow keys when the table region is focused.

Claim domains, failure conditions, and destinations across Volume XV
Domain and destination	Object and observable	State, ensemble, and conventions	Approximation, status, and evidence timing	Uncertainty, counterevidence, and falsifier	Failure condition	Licensed conclusion
Quantum-Gravity Claims, Observables, and Evidence	dictionary; saddle result; phenomenological proposal	Declare both theories and parameter map; state, contour, and expansion order; mechanism, nuisance model, and data; use the volume conventions unless the page states a local replacement.	Proposal or conditional construction. Control chain: theory pair and global data → state, algebra, and observable → claim class and regime → evidence and falsifier → bounded conclusion. Sources are cited on the destination page; literature checked through 10 August 2026.	A mapped protected observable disagrees, an omitted saddle defeats the claimed accuracy, or independent data reject the specified mechanism with nuisance errors controlled.	Inferring exact equivalence, nonperturbative completion, or a unique UV theory from one bounded test.	A quantum-gravity claim becomes testable only after its theories, observable, regime, evidence class, and falsifier are fixed.
Large N and Semiclassical Bulk Criteria	factorization; large gap; finite-N sector	Declare operator normalization and N scaling; single-trace sector and gap definition; order of N, time, and energy limits; use the volume conventions unless the page states a local replacement.	Conditional theorem or structural result. Control chain: normalized large-N data → factorization and spectrum → gap and coupling hierarchy → locality and correction tests → semiclassical-bulk criterion. Sources are cited on the destination page; literature checked through 10 August 2026.	Unsuppressed normalized cumulants, a light higher-spin tower, or order-one late-time errors defeat the corresponding weak-field, Einstein, or finite-precision claim in the declared regime.	Inferring geometric locality from factorization, a sufficient bulk criterion from a gap alone, or exact late-time behavior from an asymptotic expansion.	Factorization, sparsity, a higher-spin gap, and controlled corrections are independent criteria; large N alone does not imply Einstein gravity.
AdS Geometry, Boundary Problems, and the Dictionary	scalar mode; current or stress tensor; state dictionary	Declare mass, patch, and boundary condition; gauge group, charges, and counterterms; Euclidean cap or Lorentzian initial data; use the volume conventions unless the page states a local replacement.	Dictionary entry or correspondence claim. Control chain: AdS patch and conformal boundary → boundary and global conditions → asymptotic field modes → renormalized source and response → operator dictionary. Sources are cited on the destination page; literature checked through 10 August 2026.	The declared branch has a divergent renormalized norm or forbidden flux, the response violates its Ward identity, or the state map fails its stated inner-product test.	Using a branch outside its stability window, or promoting a local dictionary to complete global equivalence or smooth geometries for every heavy state.	An AdS/CFT entry is defined by geometry, boundary conditions, global sector, quantization branch, and normalization—not by a mass-dimension formula alone.
String, Brane, and Top-Down Constructions	brane decoupling; lower-dimensional truncation; supergravity regime	Declare charges, energy scaling, and asymptotics; retained fields and compact geometry; curvature, string scale, and string coupling; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: worldsheet and brane data → decoupling or near-horizon limit → flux and compact factors → truncation and corrections → top-down dictionary. Sources are cited on the destination page; literature checked through 10 August 2026.	Asymptotic interactions fail to decouple, an allowed lower-dimensional solution fails the parent equations on uplift, or omitted string or loop corrections become order one.	Inferring a complete finite-cutoff dictionary, the full compactified theory, or a nonperturbative definition from a controlled subsector.	Top-down control requires separate checks of decoupling, flux quantization, Kaluza-Klein scales, truncation, string corrections, and loops.
Nonperturbative String- and M-Theory Definition Proposals	matrix quantum mechanics; matrix or string field model; AdS/CFT as definition	Declare large-N limit and compactification sector; gauge fixing, background, and observables; exact boundary theory and global data; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: defining variables and action → Hamiltonian or path integral → observable and sector map → spacetime recovery tests → typed definition claim. Sources are cited on the destination page; literature checked through 10 August 2026.	A target-sector benchmark disagrees after controlled limits, a claimed amplitude fails unitarity, or a required sector has no image under the proposed complete map.	Promoting a sector-specific definition to covariant completeness, all backgrounds, or arbitrary quantum gravity.	BFSS, BMN, IKKT, matrix strings, string field theory, and AdS/CFT define different objects and satisfy different completeness tests.
Holographic Renormalization and Radial Dynamics	divergent on-shell action; one-point function; radial flow	Declare radial coordinate and induced fields; source normalization and counterterm action; cutoff surface and boundary conditions; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: Fefferman-Graham cutoff data → radial Hamilton-Jacobi recursion → local and finite counterterms → one-point functions and Ward identities → renormalized observable. Sources are cited on the destination page; literature checked through 10 August 2026.	A divergence or inadmissible variation survives counterterms, the response violates its scheme-matched Ward identity, or the proposed radial map fails canonical constraints.	Inferring scheme-independent contacts, identifying response with a bare coefficient, or equating radial evolution with Wilsonian RG without its additional dictionary.	Holographic renormalization fixes divergences but leaves declared finite schemes, boundary conditions, and contact terms in the physical answer.
Witten Diagrams and AdS Perturbation Theory	contact diagram; exchange diagram; loop diagram	Declare vertex, measure, and source normalization; field spectrum and propagator branch; regulator, counterterms, and contour; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: boundary sources and bulk action → propagators and vertices → AdS diagram integral → OPE and analytic checks → perturbative boundary correlator. Sources are cited on the destination page; literature checked through 10 August 2026.	The permutation-completed contact term has the wrong symmetry, an exchange residue disagrees with the stated spectrum, or a fixed-order cut fails after required terms are included.	Inferring a unique Lagrangian, a flat-space amplitude, or an exact finite-N correlator from a finite-radius perturbative contribution.	A Witten diagram is an AdS perturbative contribution whose normalization, boundary conditions, contact terms, and loop counterterms remain explicit.
AdS Scattering, Mellin Methods, and Bulk Locality	Mellin pole; flat-space limit; bulk locality	Declare Gamma measure, contour, and normalization; wavepackets and AdS-radius scaling; gap, Regge bound, and EFT window; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: CFT and Mellin data → exchange poles and contacts → Regge and gap controls → flat-space scaling limit → bounded locality claim. Sources are cited on the destination page; literature checked through 10 August 2026.	Mellin residues fail the declared OPE data, the scaled amplitude has the wrong scattering normalization, or finite-gap errors exceed the claimed locality window.	Inferring unique exchange, finite-radius S-matrix equality, or exact finite-gap locality from the corresponding limited diagnostic.	Mellin poles, bounded growth, a large gap, and a controlled flat limit support different parts of a bulk-scattering interpretation.
Thermal Phases and AdS Black Holes	Hawking-Page transition; charged or rotating saddle; higher-derivative entropy	Declare boundary topology and canonical ensemble; chemical potentials and regularity; covariant action and boundary terms; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: ensemble and boundary data → Euclidean gravitational saddles → action, entropy, and charges → stability and finite-N checks → thermal phase claim. Sources are cited on the destination page; literature checked through 10 August 2026.	The same-ensemble crossing is absent, the first law fails with matched charges, or stationary-horizon Wald entropy disagrees with the same-action Euclidean derivative.	Inferring a sharp finite-N transition, stability in every ensemble, or microscopic state counting from semiclassical thermodynamics.	A holographic phase is an ensemble-specific saddle comparison; classical dominance does not determine exact finite-N spectra or recurrences.
Lorentzian, Nonequilibrium, and Chaotic Holography	retarded response; quasinormal mode; scrambling or plateau	Declare source convention and infalling condition; background, channel, and boundary condition; operator ordering, N, and time limits; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: real-time contour and state → Lorentzian bulk geometry → initial and horizon conditions → poles, response, and chaos tests → time-window conclusion. Sources are cited on the destination page; literature checked through 10 August 2026.	The response precedes its source, a proposed mode fails the declared boundary problem or refinement test, or a time-window prediction disagrees with its matched benchmark.	Inferring all contour correlators, nonlinear thermalization, or exact finite-N irreversibility from one linear or time-window result.	Real-time holography depends on contour, state preparation, causal boundary conditions, and a declared time window; horizons do not fix exact late time.
Holographic Matter, Transport, and Model Building	transport coefficient; infrared scaling phase; bottom-up model	Declare current normalization and Kubo limit; matter content and boundary conditions; operator map and parameter calibration; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: bulk matter action and state → charged or scaling background → horizon and boundary response → transport and robustness tests → bounded mechanism claim. Sources are cited on the destination page; literature checked through 10 August 2026.	The response violates the applicable Ward or positivity condition, an allowed growing perturbation destroys a claimed attractor, or independent observables reject a calibrated model.	Inferring a universal material value, a microscopic phase, or a top-down UV completion from a model mechanism.	A holographic matter model can demonstrate a mechanism or universality class without identifying the microscopic theory of a material or plasma.
Bulk Reconstruction and Gravitational Dressing	HKLL field; dressed observable; subregion reconstruction	Declare free equation, patch, and normalizable modes; anchoring and gauge convention; region, code sector, and norm; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: boundary region and algebra → bulk equation and smearing → interaction and gravitational dressing → causal and error checks → reconstructable observable. Sources are cited on the destination page; literature checked through 10 August 2026.	The reconstructed field has the wrong boundary limit, its dressing changes under a boundary-trivial gauge transformation, or overlap representatives disagree beyond code-sector errors.	Inferring exact finite-N locality, strict compact support, or state-independent global locality from a qualified reconstruction.	Bulk reconstruction is always relative to a region, algebra, dressing, state sector, perturbative order, and error notion.
Holographic Entropy and Quantum Extremal Geometry	RT or HRT surface; FLM or QES; replica derivation	Declare state, region, homology, and causal setting; bulk entropy scheme and Newton coupling; integer replicas and continuation rule; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: regulated state and entropy → extremal or generalized functional → replica and surface selection → maximin and correction checks → geometric entropy claim. Sources are cited on the destination page; literature checked through 10 August 2026.	A proposed surface fails homology or extremality, a correction retains uncancelled regulator dependence, or the replica family violates its declared boundary problem.	Inferring exact finite-N entropy, microscopic factorization, or a unique nonperturbative continuation from a semiclassical prescription.	RT, HRT, FLM, and QES are distinct prescriptions with different orders in gravity, saddle choices, and renormalization requirements.
Modular Response, Relative Entropy, and Emergent-Gravity Claims	entanglement first law; relative-entropy equality; field-equation inference	Declare reference state and modular operator; boundary and bulk algebras plus area term; all balls or shapes and local dynamics assumptions; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: boundary relative entropy → modular flow and first law → bulk canonical energy → positivity and shape checks → conditional gravity inference. Sources are cited on the destination page; literature checked through 10 August 2026.	A first-law residual survives at linear order, matched relative entropies disagree beyond the retained order, or an omitted boundary term invalidates the field-equation inference.	Inferring nonlinear dynamics, equality for all states, or a unique quantum-gravity action from a conditional information identity.	Information identities constrain gravity only after the dictionary, code sector, semiclassical expansion, and boundary terms are fixed.
Entanglement Wedges and Holographic Quantum Error Correction	toy tensor code; semiclassical wedge; finite-N recovery	Declare finite Hilbert spaces and exact isometry; code subspace, center, and area term; operator class and error norm; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: code subspace and algebras → encoding and recovery maps → wedge and area-center data → error norm and finite-N test → qualified QEC claim. Sources are cited on the destination page; literature checked through 10 August 2026.	An allowed toy-code input fails exact recovery, matched code-sector relative entropies disagree, or the specified finite-N recovery map exceeds its declared norm bound.	Promoting toy-code recovery to a gravity theorem, leading reconstruction to exact isometry, or one framework to consensus on a shared logical algebra.	Exact toy-code recovery, leading semiclassical wedge reconstruction, and finite-N holographic QEC are different statements with different algebras and errors.
Holographic Complexity Proposals and Diagnostics	complexity equals volume; complexity equals action; complexity bound	Declare slice, length scale, and subtraction; WdW patch and null-boundary terms; gate set or bulk prescription; use the volume conventions unless the page states a local replacement.	Proposal or conditional construction. Control chain: boundary complexity task → CV, CA, or path proposal → regulator and counterterms → growth and switchback tests → proposal comparison. Sources are cited on the destination page; literature checked through 10 August 2026.	With boundary task and scheme fixed, a claimed cost prediction disagrees, required null-boundary cancellations fail, or an admissible state violates the proposed bound.	Equating CV with CA, assuming scheme independence, or promoting a model bound to a universal operational theorem.	CV, CA, path-integral, and tensor-network prescriptions are inequivalent conjectures whose divergences and operational meaning must be compared.
AdS3/CFT2 and Three-Dimensional Gravity	Brown-Henneaux symmetry; BTZ saddle; pure gravity proposal	Declare boundary falloffs and charge normalization; ensemble, identifications, and spin; spectrum, topology sum, and global form; use the volume conventions unless the page states a local replacement.	Proposal or conditional construction. Control chain: CFT2 and global data → AdS3 boundary conditions → Virasoro or Chern-Simons structure → BTZ and modular checks → three-dimensional gravity claim. Sources are cited on the destination page; literature checked through 10 August 2026.	Charges fail integrability under the declared falloffs, BTZ entropy fails its matched Cardy regime, or a claimed discrete unitary CFT has inadmissible degeneracies.	Inferring a complete Hilbert space, an individual BTZ geometry for every heavy state, or an established pure-gravity definition from partial control.	AdS3/CFT2 combines unusually strong symmetry with global and spectral subtleties; BTZ control does not settle pure quantum gravity.
AdS2, JT Gravity, SYK, and Random Matrices	Schwarzian mode; SYK interface; matrix completion	Declare near-AdS2 boundary condition and coupling; disorder, large N, and conformal window; ensemble and spectral density; use the volume conventions unless the page states a local replacement.	Proposal or conditional construction. Control chain: near-AdS2 boundary data → JT and Schwarzian mode → SYK low-energy matching → topology and matrix ensemble → model-specific conclusion. Sources are cited on the destination page; literature checked through 10 August 2026.	Matched infrared correlators disagree beyond omitted-order errors, or the proposed matrix ensemble fails to reproduce a stated JT genus coefficient or spectral statistic.	Inferring a full spectrum, a unique SYK–JT duality, or a unique fixed Hamiltonian from shared low-energy or ensemble data.	JT, Schwarzian dynamics, SYK, and random matrices overlap in controlled limits but do not provide one unique fixed-theory completion.
Black-Hole Microstates and Stringy Entropy	BPS index; brane microstate count; microstate geometry	Declare charges, chamber, and fermion signs; decoupling limit and charge map; smooth solution family and quantization; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: charges and protected sector → index versus degeneracy → brane count and attractor data → correction and emission checks → microstate claim. Sources are cited on the destination page; literature checked through 10 August 2026.	Index protection fails only if it changes within the same protected domain and chamber; matched entropy growth can fail independently, and undersized quantized families defeat completeness claims.	Promoting an index to degeneracy in every regime, a special geometry to typical non-BPS physics, or a partial family to the full Hilbert space.	Protected indices, actual degeneracies, typical states, and non-BPS microstates must remain distinct when compared with black-hole entropy.
Wormholes, Gravitational Path Integrals, and Ensembles	Euclidean wormhole; replica wormhole; factorization statement	Declare boundary data, measure, and cycle; replica boundary conditions and continuation; fixed theory, ensemble, or alpha sector; use the volume conventions unless the page states a local replacement.	Conditional theorem or structural result. Control chain: boundary conditions and contour → saddles and negative modes → topology or replica sum → factorization and alpha-sector tests → completion claim. Sources are cited on the destination page; literature checked through 10 August 2026.	The chosen cycle gives a saddle zero weight, a replica contribution fails normalization, or independent fixed-theory boundary copies retain a connected term where factorization was claimed.	Inferring path-integral convergence, microscopic evaporation dynamics, or automatic ensemble averaging from a wormhole contribution.	A wormhole contribution is defined only with a contour and theory; connected boundaries do not by themselves establish an ensemble or a fixed-theory completion.
Black-Hole Information, Islands, and Interiors	Page curve; island saddle; interior reconstruction	Declare unitary benchmark and radiation factorization; bath coupling, QES functional, and replicas; code sector, state dependence, and algebra; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: evaporation model and radiation algebra → replicas and generalized entropy → island and wedge selection → Page, decoding, and interior tests → microscopic ceiling. Sources are cited on the destination page; literature checked through 10 August 2026.	Entropy disagrees with the declared benchmark, an admissible extremum defeats the selected island, or interior representatives disagree beyond the declared code-sector error.	Inferring a microscopic S-matrix, unique completion, or observer-independent exact interior operators from a semiclassical entropy calculation.	Islands can produce semiclassical Page curves and radiation wedges without supplying microscopic evaporation dynamics, decoding, interiors, or endpoints.
Higher-Spin and Vector-Model Holography	higher-spin dictionary; alternate boundary condition; symmetry breaking	Declare boundary model, parity phase, and global data; scalar branch and double-trace flow; coupling and anomalous dimensions; use the volume conventions unless the page states a local replacement.	Dictionary entry or correspondence claim. Control chain: vector-model large-N data → higher-spin algebra and fields → boundary conditions and correlators → breaking and tensionless tests → non-Einstein bulk regime. Sources are cited on the destination page; literature checked through 10 August 2026.	Normalized correlators or flow endpoints disagree, or the stated anomalous dimensions fail the deformation test; a surviving light higher-spin tower blocks an Einstein promotion.	Inferring Einstein gravity, an unchanged all-order bulk theory, or an automatic string completion from higher-spin matching.	Higher-spin/vector-model dualities define controlled non-Einstein regimes; restoring a large higher-spin gap is a separate dynamical problem.
de Sitter and Cosmological Holography	late-time wavefunction; in-in correlator; static-patch proposal	Declare state, boundary data, and phase convention; closed-time contour and operator ordering; observer algebra and horizon state; use the volume conventions unless the page states a local replacement.	Proposal or conditional construction. Control chain: de Sitter state and observer patch → wavefunction or in-in observable → analytic continuation and dictionary → entropy and static-patch tests → proposal status. Sources are cited on the destination page; literature checked through 10 August 2026.	Wavefunction coefficients violate the applicable Ward identity, a Hermitian in-in observable becomes nonreal, or an observer state fails positivity or its claimed thermal relation.	Identifying wavefunctions with ordinary CFT probabilities or in-in correlators, or promoting a patch description to a complete global dual.	Late-time wavefunctions, in-in correlators, and static-patch observables are different objects; no single continuation supplies a complete de Sitter dual.
Flat-Space, BMS, and Celestial Holography	asymptotic symmetry; celestial transform; celestial OPE	Declare falloffs, charges, and phase space; basis, contour, and infrared dressing; operator basis, loop order, and regulator; use the volume conventions unless the page states a local replacement.	Proposal or conditional construction. Control chain: null-infinity states and data → BMS, soft, and dressing sectors → celestial transform and OPE → loop, unitarity, and completeness tests → flat-holography status. Sources are cited on the destination page; literature checked through 10 August 2026.	The declared soft Ward identity disagrees, the inverse celestial transform fails in its domain, or the OPE misses the required collinear residue at the stated order.	Inferring a complete dual, standalone local CFT, or nonperturbative completeness from asymptotic or transformed scattering data.	A flat-space S-matrix, its celestial transform, BMS charges, and a complete celestial dual are distinct layers of a proposed dictionary.
Quantum-Gravity Consistency and Swampland	no global symmetry; weak gravity or distance conjecture; de Sitter or landscape claim	Declare exact AdS/CFT or other stated premise; charge normalization or moduli metric; compactification and EFT assumptions; use the volume conventions unless the page states a local replacement.	Named conjecture under stated hypotheses. Control chain: quantum-gravity premise and black holes → charge, tower, and moduli constraints → examples and conditional derivations → counterexamples and dated tests → typed consistency claim. Sources are cited on the destination page; literature checked through 10 August 2026.	A proposed theorem application lacks a required premise, a controlled example violates a named conjecture’s hypotheses-qualified prediction, or omitted corrections defeat an exclusion argument.	Presenting a conditional theorem as assumption-free, a conjecture as a proven inequality, or a scoped obstruction as absence of all vacua.	No-global-symmetry results and swampland conjectures have different hypotheses and evidence; examples do not erase counterexamples or dates.
Canonical, Loop, Spin-Foam, and Group-Field Quantum Gravity	area or volume spectrum; spin-foam amplitude; semiclassical recovery	Declare kinematical Hilbert space and operator choice; boundary state, model, and refinement; state family and coarse graining; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: constrained phase space → connections and spin networks → Hamiltonian, foam, or group-field dynamics → continuum and semiclassical tests → physical-observable claim. Sources are cited on the destination page; literature checked through 10 August 2026.	A proposed operator fails its declared gauge domain, a foam amplitude misses its stated constraints or Regge regime, or claimed Einstein observables fail controlled refinement.	Promoting kinematical discreteness to a physical measurement, a model amplitude to continuum dynamics, or sector recovery to full phenomenology.	Kinematical discreteness, constraint solutions, spin-foam amplitudes, continuum limits, and classical recovery are separate achievements.
Asymptotic Safety, Causal, and Discrete Quantum-Gravity Programs	asymptotic-safety fixed point; triangulation or causal-set limit; spectral dimension flow	Declare effective action, gauge, regulator, and truncation; ensemble, measure, and refinement rule; diffusion operator and averaging; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: RG or discrete defining data → regulator, truncation, or refinement → continuum scaling observables → unitarity and causality tests → UV-completion claim. Sources are cited on the destination page; literature checked through 10 August 2026.	A fixed-point claim fails controlled truncation checks, continuum observables fail their stated scaling, or a diffusion flow fails matched-scale refinement tests.	Promoting a truncation fixed point to a proven UV completion, one continuum sector to all Einstein observables, or spectral dimension to physical dimension alone.	A fixed point in a truncation or a continuum-looking phase in a discrete model is evidence that requires regulator, convergence, and unitarity control.
Quantum Cosmology and Singularity-Resolution Programs	Wheeler-DeWitt solution; loop-cosmology bounce; singularity resolution	Declare inner product, boundary condition, and clock; difference equation and effective regime; operational criterion and observable; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: cosmological state and constraint → clock and boundary condition → minisuperspace or effective dynamics → decoherence and full-theory tests → qualified resolution claim. Sources are cited on the destination page; literature checked through 10 August 2026.	A proposed probability is not positive and normalized in the declared physical product, bounce control fails in its model, or a claimed resolution retains finite-time curvature divergence.	Inferring a unique cosmology from a wavefunction, full inhomogeneous resolution from a homogeneous bounce, or every singularity criterion from one bounded variable.	A wavefunction, effective bounce, bounded variable, geodesic extension, and full singularity resolution are different claims.
Quantum-Gravity Phenomenology and Comparative Status	modified propagation; gravity-mediated entanglement; compact-object or cosmological signal	Declare EFT operator, source model, and distance; locality, mediation, and noise assumptions; waveform or primordial model and nuisance priors; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: mechanism and detector observable → data and nuisance model → likelihood and systematics → competing explanations → bound, anomaly, or detection. Sources are cited on the destination page; literature checked through 10 August 2026.	A propagation pattern fails independent-source tests, a witness does not establish the claimed mediation, or a proposed anomaly disappears under calibrated systematics.	Inferring a unique UV completion, selecting a quantum-gravity program, or claiming confirmed quantum gravity without applicable alternative tests.	Quantum-gravity phenomenology begins with a mechanism and likelihood; sensitivity, bounds, anomalies, and detections have sharply different meanings.

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Where to go next

For the boundary theory’s operator data and crossing constraints, use Conformal Field Theory and Bootstrap. For supersymmetric constructions and protected quantities, use Supersymmetry and Duality.
For matter fields and controlled gravitational approximations, use QFT in Curved Spacetime. For entropy and recovery independently of holography, use Quantum Information in QFT.
For precise mathematical formulations, use Mathematical QFT. For changing evidence and open questions, use the holography and quantum-gravity research field.

References

Harlow, Daniel. 2018. “TASI Lectures on the Emergence of Bulk Physics in AdS/CFT.” Proceedings of Science TASI2017: 002. DOI. Open text, arXiv:1802.01040v3.
Witten, Edward. 1998. “Anti-de Sitter Space and Holography.” Advances in Theoretical and Mathematical Physics 2: 253–291. DOI. Open PDF.