Evidence Programs for Holographic Duality
No single celebrated match establishes a holographic dictionary. A persuasive evidence program probes different entries with calculations whose premises and systematic errors are sufficiently independent: anomalies, protected spectra, unprotected thermodynamics, dynamical correlators, integrability, and numerical observables answer different questions.
Required background. Holographic Duality: Claims, Dictionaries, and Regimes fixes what is being tested, and Exact Statements, Saddle Expansions, and Conditional Derivations fixes the logical status of each comparison.
Helpful background. Exact-Observable Identities as Duality Tests develops protected tests; AGT and Exact-Correspondence Dictionaries: Status and Limits supplies a correspondence-level comparison; Anomaly Polynomials and Inflow supplies structural anomaly tests; and Benchmark Reproduction and Data Provenance supplies numerical verification practice.
What makes a test informative
Section titled “What makes a test informative”For each comparison , record
where is the observable, the hypotheses, the method, its uncertainty, and a possible failure signature. Two results are not independent merely because they appear in different papers.
An effective program combines:
- structural tests, such as symmetry and anomaly matching;
- protected tests, whose coupling dependence is controlled by supersymmetry or topology;
- unprotected analytic tests, such as thermal free energies or dynamical correlators in overlapping regimes;
- spectral and integrability tests, where exact or high-order data are available;
- numerical tests, with continuum extrapolation and reproducible uncertainty;
- failure tests, designed to distinguish a wrong dictionary from a failed approximation.
Evidence for AdS5/CFT4
Section titled “Evidence for AdS5/CFT4”The canonical example illustrates both breadth and dependence.
| Test | Dictionary component probed | Main shared premise or limitation |
|---|---|---|
| Conformal and R-symmetry anomalies | Normalization of currents and the stress tensor | Protected, hence narrow |
| BPS spectra and indices | Charge map and protected state sectors | Insensitive to cancellations among long multiplets |
| Wilson loops | Extended-operator and string-worldsheet map | Often uses supersymmetry or localization |
| Strong-coupling thermal free energy | Unprotected many-body dynamics | Computed in a large-, strong-coupling regime |
| Integrable spectral data | Detailed planar anomalous dimensions | Planar limit and integrable subsector assumptions |
| Four-point functions | Interactions, exchange spectrum, and locality | Truncation in and inverse coupling |
The near-extremal D3-brane entropy calculation of Gubser, Klebanov, and Peet 1996 gives a strong-coupling result that differs from the free-field value by a factor approaching in the supergravity regime. This is not an exact equality across coupling; it demonstrates controlled interpolation targets and nontrivial scaling.
Counting dependencies, not papers
Section titled “Counting dependencies, not papers”Suppose an anomaly, a protected index, and a Wilson loop are all evaluated using the same supersymmetric localization framework and the same parameter identification, as in the exact sphere framework of Pestun 2012. They remain distinct observables, but their methodological and dictionary premises overlap. Removing all results derived from one localization identity should reduce the evidence count by one dependency class rather than by the number of plots or observables generated from it.
By contrast, a lattice calculation of an unprotected quantity with an independent continuum limit can add genuinely new information even if its precision is lower. Independence is about causal derivation and calibration, not prestige or numerical accuracy alone.
What survives the adversarial removal
Section titled “What survives the adversarial removal”Remove every protected result that shares the same supersymmetric identity. The remaining anomaly constraints, unprotected thermodynamics, dynamical correlators, and independently reproduced numerical data still support specified parts of the dictionary. They do not by themselves prove finite-, all-coupling equivalence. A reliable conclusion names exactly which map entries have been tested and which rest on extrapolation.
Evidence cutoff. This evidence classification is fixed to 25 July 2026. Mutable assessments and contrary literature belong in Research.
The chapter overview contains the structure diagram and validity and failure diagram. They are embedded there once so that their shared chapter-level context is not repeated on every article.
For the chapter-wide comparison of assumptions, counterevidence, falsifiers, and claim ceilings, see the claim-domain table.
References
Section titled “References”- Beisert, Niklas, Changrim Ahn, Luis F. Alday, et al. 2012. “Review of AdS/CFT Integrability: An Overview,” Letters in Mathematical Physics 99, 3–32.
- Gubser, Steven S., Igor R. Klebanov, and Amanda W. Peet. 1996. “Entropy and Temperature of Black 3-Branes,” Physical Review D 54, 3915–3919.
- Henningson, Måns, and Kostas Skenderis. 1998. “The Holographic Weyl Anomaly,” Journal of High Energy Physics 07, 023.
- Pestun, Vasily. 2012. “Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops,” Communications in Mathematical Physics 313, 71–129.