| AdS/CFT correspondence | |
|---|---|
| Name | AdS/CFT correspondence |
| Field | Theoretical physics |
| Introduced | 1997 |
| Proponents | Juan Maldacena |
| Related | Gauge–gravity duality; Holographic principle |
AdS/CFT correspondence
The AdS/CFT correspondence is a conjectured duality between a gravitational theory in a higher-dimensional spacetime with asymptotic anti–de Sitter (AdS) boundary conditions and a conformal field theory (CFT) living on that boundary. It provides a nonperturbative formulation of certain quantum gravity models and a concrete realization of the Holographic principle, with deep implications for understanding strongly coupled Quantum field theory and black hole thermodynamics.
The correspondence was proposed by Juan Maldacena in 1997 as a precise example of a more general gauge–gravity duality. In its original form it relates type IIB string theory on AdS5 × S^5 to N=4 supersymmetric Yang–Mills theory in four dimensions. Physically, the duality maps bulk gravitational dynamics, including black hole formation and Hawking radiation, to unitary evolution in a lower-dimensional quantum field theory, providing insight into the black hole information paradox and the emergence of spacetime. In condensed-matter and nuclear theory, AdS/CFT gives tools to study strongly correlated systems and the quark–gluon plasma produced in RHIC and LHC experiments.
The core statement identifies the partition function of the bulk gravitational/string theory with the generating functional of correlation functions of the boundary CFT. Symbolically, Z_bulk[φ_boundary] = ⟨exp(∫ φ_boundary O)⟩_CFT. Key elements of the dictionary include the matching of symmetries: the isometry group of Anti-de Sitter space corresponds to the conformal group of the boundary CFT. Bulk fields map to local operators (e.g., the bulk metric ↔ the CFT energy–momentum tensor), and bulk radial evolution is associated with renormalization group flow in the boundary theory. The correspondence leverages tools from conformal symmetry, supersymmetry, and string theory to establish operator/state maps, correlator computations, and spectral matching via Kaluza–Klein reductions on compact manifolds like S^5.
The best-studied example is the AdS5/CFT4 duality between type IIB superstring theory on AdS5 × S^5 and N=4 supersymmetric Yang–Mills theory with gauge group SU(N) in the large-N limit; here the string coupling and the 't Hooft coupling λ control the map between classical supergravity and strongly coupled gauge theory. Another canonical case is AdS3/CFT2, which relates gravity in three-dimensional AdS space to two-dimensional conformal field theories; this setting connects to Brown–Henneaux central charge calculations and the analytic control of 2D CFTs, such as those described by the Virasoro algebra. Lower-dimensional examples include AdS2/CFT1 and dualities relevant to near-horizon dynamics of extremal black holes and to the Sachdev–Ye–Kitaev model as a toy model for nearly-AdS2 gravity.
AdS/CFT remains a conjecture supported by extensive nontrivial checks rather than a formal proof. Evidence includes matching of symmetries, spectra, and correlation functions computed perturbatively on both sides, agreement of protected quantities such as BPS spectra and anomalous dimensions computed via integrability techniques, and thermodynamic matches like the Bekenstein–Hawking entropy of certain supersymmetric black holes with degeneracies obtained from boundary CFT counting (e.g., Strominger–Vafa microstate counting). Additional checks arise from comparisons of scattering amplitudes, Wilson loop expectation values computed via minimal surfaces in AdS, and successful use of AdS/CFT correspondence technology in computing transport coefficients (e.g., the shear viscosity to entropy density ratio η/s) that agree qualitatively with quark–gluon plasma observations. Methods contributing checks include string perturbation theory on AdS backgrounds, holographic renormalization, and integrability in planar N=4 SYM.
AdS/CFT is a working laboratory for quantum gravity. It provides a controlled setting for investigating spacetime emergence, entanglement entropy as a probe of geometry (e.g., the Ryu–Takayanagi formula), and the role of quantum information in gravitational dynamics. The correspondence has inspired developments in entanglement wedge reconstruction, quantum error correction interpretations of holography, and concrete models for evaporating black holes that address unitarity. In high-energy physics, AdS/CFT techniques model strongly coupled QCD-like plasmas (holographic QCD), while in condensed-matter physics, holographic duals are used to study non-Fermi liquids, superconductivity, and quantum critical transport.
Generalizations include gauge/gravity dualities beyond AdS geometries, such as dualities involving asymptotically flat spacetimes, de Sitter proposals, and nonconformal field theories via warped or domain-wall geometries and the use of holographic renormalization group flows. Top-down constructions derive holographic duals from string/M-theory compactifications; bottom-up "AdS/QCD" and "AdS/CMT" models build effective bulk theories to capture phenomenology. Limitations include the restriction of rigorous control often to supersymmetric, large-N, or planar limits and to theories with a classical gravity dual; extending holography to realistic cosmological spacetimes (e.g., de Sitter space) remains unresolved. Open problems include a microscopic derivation of bulk locality, precise criteria for when a CFT admits a weakly curved gravity dual, and a full nonperturbative definition of string theory in AdS that reproduces all boundary observables.
Category:String theory Category:Holography Category:Quantum gravity