Holography and Quantum Gravity
Holography and quantum-gravity research asks when a nongravitational quantum theory encodes a gravitational spacetime and what can be learned about bulk locality, black holes, and cosmology. The best-controlled domain is gauge/gravity duality with asymptotically anti-de Sitter (AdS) boundary conditions, large effective , and often strong coupling. This guide includes dictionary tests, reconstruction, entropy, gravitational path integrals, and non-AdS extensions; it excludes treating semiclassical bulk intuition as a definition of the exact boundary theory.
Evidence cutoff. 11 August 2026.
Required background. The GKPW dictionary supplies the source/operator relation, dictionary completeness and global data states what a duality must match, and large-N factorization explains semiclassical scaling.
Helpful background. Finite-N and horizon reconstruction limits scopes bulk operators, operator-algebra QEC supplies reconstruction language, large-gap locality tests gives CFT-side diagnostics, and quantum extremal surfaces states the semiclassical entropy object.
A hierarchy of holographic dictionary control
Section titled “A hierarchy of holographic dictionary control”| Program | Strongly controlled claim | Additional assumptions | Present ceiling |
|---|---|---|---|
| top-down AdS/CFT | matched symmetries, spectra/protected data, large-N correlators in specific constructions | decoupling limit and exact identification of global data | generic finite-coupling and finite-N observables remain hard |
| effective bulk reconstruction | local fields represented in a boundary code subspace | semiclassical background, perturbative , restricted states | no state-independent exact local bulk algebra across all states |
| entanglement-wedge reconstruction | algebra recovery from boundary subregions | entropy formula and code-subspace conditions | quantum/finite-N corrections and phase transitions complicate reconstruction |
| black-hole path integrals | saddle contributions to partition functions or replica observables | contour, ensemble, topology, boundary conditions | factorization and microscopic interpretation can be unresolved |
| flat/dS/celestial programs | asymptotic observables and proposed dictionaries | boundary conditions and completion-specific structures | less complete nonperturbative definitions than standard AdS/CFT |
Maldacena’s proposal and the GKPW relation give a precise family of observable maps, not merely a geometric analogy Maldacena 1998, foundational proposal Gubser, Klebanov, and Polyakov 1998, foundational dictionary. Evidence is layered: symmetry and protected-spectrum matches, anomaly and central-charge matches, integrability/localization checks, thermal phase structure, and dynamical correlators. Several derive from the same supersymmetric protection and should not be counted as independent confirmations.
Reconstruction, entropy, and black holes
Section titled “Reconstruction, entropy, and black holes”HKLL reconstruction represents perturbative bulk fields through smeared boundary operators in a fixed semiclassical setting Hamilton et al. 2006, method. Quantum-error-correction language explains why the same bulk operator can have multiple boundary reconstructions and why a code subspace is essential Almheiri, Dong, and Harlow 2015, method. Neither result provides exact finite-N locality behind arbitrary horizons.
Replica-wormhole and island calculations reproduce a Page-curve-shaped entropy in controlled semiclassical models and effective setups Penington 2020, island and entanglement-wedge result. They are strong evidence about the generalized-entropy saddle calculation; they do not alone identify the microstates of a single evaporating four-dimensional black hole or settle ensemble/factorization questions in every model. JT gravity supplies a concrete case in which the gravitational genus expansion is identified with a matrix-integral expansion Saad, Shenker, and Stanford 2019, JT-gravity matrix-integral construction. A gravitational path integral that averages theories can compute a sensible quantity while failing to be the partition function of one fixed boundary Hamiltonian.
Validation requires dictionary-level comparison, not matching qualitative curves. Record the boundary theory, global form, state or ensemble, and coupling regime, operator normalization, bulk boundary conditions, saddle contour, loop order, and error from neglected saddles. Begin by recovering the scalar mass–dimension relation and the normalization of a boundary two-point function, then compare contact and exchange Witten diagrams with crossing and OPE limits. Entropy calculations should reproduce extremal surfaces for known AdS regions, including homology and competing-saddle transitions; top-down claims should display the explicit hierarchy among curvature, string, Kaluza–Klein, and quantum scales.
Obstructions and contrary lessons
Section titled “Obstructions and contrary lessons”Large is insufficient for an Einstein-like local bulk: sparse low-dimension spectra and appropriate correlator bounds are also needed. Bulk reconstruction is limited by gauge constraints, gravitational dressing, code-subspace size, and finite-N nonperturbativity. Euclidean saddles need a contour and can possess negative modes. Black-hole entropy agreement is not automatically evidence for a unique microscopic realization.
Factorization supplies a decisive negative test: two disconnected boundaries in a fixed boundary theory should give a product, while connected bulk saddles appear to correlate them. Ensemble interpretations resolve this in some lower-dimensional models but cannot be silently transferred to every AdS/CFT pair. Non-AdS holography remains a portfolio of programs rather than one established dictionary.
Entering the field
Section titled “Entering the field”Choose a single dictionary entry and verify it at leading order and one controlled correction. Track which step uses large , strong coupling, supersymmetry, a code subspace, or saddle dominance. The gravity/cosmology pathway and claim-tracing module are suitable entry points.
This guide omits speculative quantum-gravity constraints that lack a defined observable and comparator. It treats tensor-network toy models as conceptual benchmarks, not direct evidence for a microscopic gravity theory.
Evidence scope and related assessments
Section titled “Evidence scope and related assessments”The finite search used arXiv, INSPIRE, journal/DOI records, top-down construction and black-hole literature, and targeted searches for factorization, state-dependence, and ensemble qualifications. Sources public through 11 August 2026 were eligible. Reassess when a finite-N reconstruction result changes locality scope, a path-integral completion resolves or sharpens factorization, or a non-AdS dictionary gains decisive observable tests.
Continue to islands and unitary evaporation, bulk reconstruction beyond code subspaces, or the holographic reconstruction method map.
References
Section titled “References”- A. Almheiri, X. Dong, and D. Harlow, “Bulk Locality and Quantum Error Correction in AdS/CFT,” JHEP 04 (2015) 163. DOI.
- S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, “Gauge Theory Correlators from Non-Critical String Theory,” Physics Letters B 428 (1998) 105–114. DOI.
- A. Hamilton, D. Kabat, G. Lifschytz, and D. A. Lowe, “Local Bulk Operators in AdS/CFT: a Boundary View of Horizons and Locality,” Physical Review D 74 (2006) 066009. DOI.
- J. Maldacena, “The Large- Limit of Superconformal Field Theories and Supergravity,” Advances in Theoretical and Mathematical Physics 2 (1998) 231–252. DOI.
- G. Penington, “Entanglement Wedge Reconstruction and the Information Paradox,” JHEP 09 (2020) 002. DOI.
- P. Saad, S. H. Shenker, and D. Stanford, “JT Gravity as a Matrix Integral,” preprint arXiv:1903.11115 [hep-th] (2019). arXiv.