Quantum-Gravity Consistency and Swampland
Quantum-gravity consistency arguments ask which low-energy theories can arise from a complete gravitational theory. This chapter connects symmetry, charge, moduli-space, and cutoff constraints while keeping conditional theorems, conjectures, and examples distinct.
Enter this chapter
Section titled “Enter this chapter”Begin with Quantum-Gravity Consistency Claims and Comparison Contract to identify the theory class and quantifiers behind a proposed constraint.
Helpful background. Effective Field Theory of Gravity: Architecture and Power Counting and Low-Energy Constraints on UV Completion supply gravitational power counting and the scope of low-energy consistency tests.
Topics
Section titled “Topics”- Quantum-Gravity Consistency Claims and Comparison Contract — Distinguishes conditional deductions from patterns in controlled examples.
- No-Global-Symmetry and Compactness Results Conditional on AdS/CFT — States the holographic hypotheses behind symmetry and compactness results.
- Charge-Lattice and Gauge-Completeness Conjectures and Tests — Separates allowed charges, dynamical charges, and black-hole discharge.
- Weak-Gravity Conjectures and Their Variants — Compares inequivalent electric, magnetic, and lattice versions of weak gravity.
- Distance Conjectures, Towers, and Infinite-Distance Limits — Relates infinite moduli-space distance to conjecturally light towers.
- Species Bounds, Cutoffs, and Scale Separation — Counts species self-consistently when estimating the gravitational cutoff.
- Emergence Proposals for Gauge and Gravitational Couplings — Separates calculable threshold corrections from assumptions about ultraviolet terms.
- de Sitter Constraints and Vacuum-Structure Claims — Distinguishes restricted no-go theorems from broader de Sitter conjectures.
- Landscape and Swampland Evidence Grammar — Explains how constructions, exclusions, and surveys support different conclusions.
- Cobordism Conjecture and Topological-Sector Completeness — Tests completeness of topological sectors with specified background structures.
- Dated Status, Counterexamples, and Falsifiers — Tracks how counterexamples or altered hypotheses change a claim.
How the ideas fit together
Section titled “How the ideas fit together”A tower becoming light can undermine an effective theory before any one coupling grows large: additional species change the cutoff and the fields that must be retained. Distance, species, and emergence arguments therefore interact, but they are not equivalent statements. Threshold corrections can be computed for a specified tower without proving that all ultraviolet kinetic terms vanish. Similarly, a no-go theorem applies to its hypothesis class, while a broader conjecture requires separate tests. The distinctions and their compactification setting are developed in van Beest et al. 2022, § 1.
Claim-domain comparison
Section titled “Claim-domain comparison”Compare the assumptions and strongest supported conclusion for each case.
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| Claim object | State, ensemble, and conventions | Approximation, status, and evidence timing | Uncertainty and counterevidence | Falsifier | Failure condition | Licensed conclusion |
|---|---|---|---|---|---|---|
| no global symmetry | Declare exact AdS/CFT or other stated premise; use the volume conventions unless the page states a local replacement. | Conditional theorem or structural result. 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. | Track omitted corrections, alternate branches, and competing definitions. A failed “boundary current and bulk gauge check” check is counterevidence to the promoted claim. | A proposed application lacks the exact dictionary, symmetry action, or reconstruction premise used by the argument; the conditional theorem then cannot establish that application. | Presenting a conditional no-global-symmetry result as an assumption-free theorem about all gravity. | a conditional result in that framework |
| weak gravity or distance conjecture | Declare charge normalization or moduli metric; 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. | Track omitted corrections, alternate branches, and competing definitions. A failed “extremality, towers, and examples” check is counterevidence to the promoted claim. | A controlled example satisfying the named variant’s hypotheses violates its charge-to-mass or asymptotic tower prediction after the spectrum and moduli metric are fixed. | Presenting a named conjectural constraint as a proven universal inequality. | a named conjectural constraint |
| de Sitter or landscape claim | Declare compactification and EFT assumptions; use the volume conventions unless the page states a local replacement. | Model-specific calculation or conditional result. 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. | Track omitted corrections, alternate branches, and competing definitions. A failed “controlled examples and counterexamples” check is counterevidence to the promoted claim. | A controlled vacuum meets every hypothesis of the claimed exclusion yet exists, or an omitted correction invalidates the control needed for that exclusion. | Promoting a conditional obstruction to settled absence of all vacua. | a dated conditional exclusion or obstruction |
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Where to go next
Section titled “Where to go next”Continue to Canonical, Loop, Spin-Foam, and Group-Field Quantum Gravity to examine constructions that address dynamics and physical observables directly.