Gauge/Gravity Duality

Overview

Gauge/gravity duality — the conjecture that certain quantum gauge theories in $d$ spacetime dimensions are equivalent to theories of quantum gravity (typically string theory) on a $(d+1)$-dimensional asymptotically anti-de Sitter (AdS) spacetime — is, since Maldacena’s 1997 proposal, one of the central organising frameworks of modern theoretical physics. In its sharpest form, the AdS/CFT correspondence identifies the boundary CFT’s algebra of single-trace operators at large $N$ with the bulk gravitational algebra in a specific subregion (the entanglement wedge), so that every state and every operator on one side has a counterpart on the other.

Status in this wiki. Gauge/gravity duality is not a primary research line for the group. It is exploratory / adjacent: it sits next to the Bell inequalities in QFT and relative entropy in QFT programs as a structural source of concepts (in particular, the type III₁ algebra of single-trace operators at large $N$) and as a target of speculation (whether the Bell-CHSH and modular tools developed for flat-space QFT can probe boundary subalgebras of holographic CFTs — see bell-chsh-in-holographic-setting).

This area page is the home of a two-semester graduate course, Holography through Quantum Information and Operator Algebras, and a scaffold for the concept pages that its lecture notes reference. The course begins with recoverable information, modular structure and entropy in finite quantum systems, passes through continuum algebras and the holographic dictionary, and ends with black holes, islands and the algebras of large-$N$ theories; its notes carry explicit connections to the group’s research programs. It replaced on 2026-10-01 the earlier course built over adscft.org.

Key Results

• Maldacena’s conjecture (1997). $\mathcal{N}=4$ SU($N$) super-Yang–Mills in 4d $\leftrightarrow$ Type IIB superstring theory on ${\mathrm{AdS}}_5\times S^5$. The first concrete realisation of gauge/gravity duality.
• GKP-Witten formula (1998). $Z_{\text{CFT}}[J]=Z_{\text{gravity}}[\varphi {|}_{\partial }=J]$ — see gkp-witten-formula. The operational dictionary that turns bulk classical computations into boundary correlators.
• Large-$N$ factorization. Single-trace boundary operators are generalized free fields at $N=\infty$; their algebra is type III₁ — see large-n-factorization and type-iii-von-neumann-algebras.
• Ryu-Takayanagi formula (2006). Holographic entanglement entropy from minimal-area extremal surfaces in the bulk — see ryu-takayanagi-formula.
• Quantum extremal surfaces / island formula (2019). Resolution of the black-hole information puzzle in semiclassical gravity coupled to a bath — see quantum-extremal-surfaces and page-curve.
• JT gravity as a soluble laboratory. 2d dilaton gravity with a calculable boundary CFT (Schwarzian theory) — see jt-gravity.
• Subregion-subalgebra duality. Bulk regions correspond to boundary subalgebras; the duality refines entanglement-wedge reconstruction at the level of algebras — see subregion-subalgebra-duality.

Open Problems

• bell-chsh-in-holographic-setting — Can Bell-CHSH and relative-entropy techniques probe holographic spacetime structure?
• bell-chsh-across-traversable-wormhole — Does opening a traversable wormhole (GJW coupling) degrade the Bell-CHSH violation between its two sides?
• relative-entropy-wormhole-opening — What is the Araki-Uhlmann relative entropy of the GJW double-trace deformation, treated as a Connes cocycle, in a free-field analogue?
• relative-entropy-interacting-theories — Can the Araki-Uhlmann relative entropy program be extended beyond free field theories, including in holographic CFTs?
• The interpretive status of the island formula and whether it admits a fully algebraic derivation parallel to crossed-product-construction.
• Whether bulk reconstruction beyond the entanglement wedge can be made precise.

Key Concepts

• holographic-dictionary
• gkp-witten-formula
• large-n-factorization
• ryu-takayanagi-formula
• quantum-extremal-surfaces
• replica-trick-gravity
• jt-gravity
• page-curve
• subregion-subalgebra-duality
• type-iii-von-neumann-algebras
• crossed-product-construction
• tomita-takesaki-modular-theory
• thermofield-double-state
• er-epr
• traversable-wormholes

Key Papers

Ingested:

• 2021-kundu-wormholes-holography — Kundu, Wormholes & Holography: An Introduction (arXiv:2110.14958; EPJC 82, 447, 2022). 89-page pedagogical review of Euclidean and traversable wormholes, the TFD/eternal-black-hole picture, replica wormholes, and GJW/Maldacena–Qi traversability.
• 2026-goto-rethinking-qi-gravity-fields — Goto et al., Rethinking quantum information in gravity and fields (arXiv:2606.30853, 2026). Nine-author open-problems agenda at the gravity/QI interface (operational characterization, observers, QEC, infinite-dimensional Hilbert spaces); its type II–III / operational-characterization themes map directly onto the group’s programs — see gravity-qi-open-problems.

Paper-page candidates (to be ingested as the course is taught — see the course reading map and the older catalogue wiki/courses/ads-cft-course/appendices/bibliography-and-paper-map.md):

• Maldacena 1997 — The large-N limit of superconformal field theories and supergravity (arXiv:hep-th/9711200).
• Gubser, Klebanov, Polyakov 1998 — Gauge theory correlators from non-critical string theory (arXiv:hep-th/9802109).
• Witten 1998 — Anti-de Sitter space and holography (arXiv:hep-th/9802150).
• Aharony, Gubser, Maldacena, Ooguri, Oz 2000 — Large $N$ field theories, string theory and gravity (Phys. Rep. 323).
• McGreevy 2009 — Holographic duality with a view toward many-body physics (arXiv:0909.0518).
• Harlow 2018 — TASI lectures on the emergence of bulk physics in AdS/CFT (arXiv:1802.01040).
• Ryu, Takayanagi 2006 — Holographic derivation of entanglement entropy from AdS/CFT (PRL 96, 181602).
• Penington 2019 — Entanglement wedge reconstruction and the information paradox (arXiv:1905.08255).
• Almheiri, Engelhardt, Marolf, Maxfield 2019 — The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole (arXiv:1905.08762).
• Maldacena, Qi 2018 — Eternal traversable wormhole (arXiv:1804.00491).
• 2025-liu-lectures-entanglement-vna — Liu’s review of entanglement, von Neumann algebras, and emergence of spacetime (arXiv:2510.07017).

General reference: xiyin-qft-monograph — Vol V (Conformal Field Theory) for the CFT-side foundations. (QFT-focused; does not cover holographic RT/QES, islands, or the Page curve.)

Connections

• bell-inequalities-qft — type III₁ algebras of subregions are the natural setting for both Bell-CHSH analyses (flat space) and holographic boundary subalgebras (large-$N$ AdS/CFT).
• relative-entropy-qft — Araki-Uhlmann relative entropy is well-defined on the type III₁ boundary algebras and connects to gravitational generalised entropy via the crossed-product-construction.
• type-iii-algebras-across-areas — the holographic side joins flat-space QFT and Rindler as a third home of type III₁.
• holographic-bell-program (new) — speculative connection asking what specifically the Bell-CHSH machinery says about boundary subalgebras at large $N$.
• crossed-product-and-island-formula (new) — both involve dressing/regulating a type III₁ algebra; one ends in a generalized entropy, the other in an island.
• wormholes-and-quantum-information-qft (new) — the wormhole/traversability story of Kundu’s review mapped onto the group’s flat-space Bell-CHSH, relative-entropy, and embezzlement programs via the TFD = two-wedge identification.
• gravity-qi-open-problems (new) — Goto et al.’s gravity/QI open-problems agenda mapped onto the group’s OQP roadmap and toolkit; an independent, holography-side confirmation that operational characterization and QI in infinite dimensions are the live frontiers.
• 2026 Algebraic-QFT course (Estrutura Algébrica da Teoria Quântica de Campos) — Semester II of the AQFT course covers Witten 2022 / CPW / AAJ, which use exactly the large-$N$ type III₁ structure of this area as their starting point.