AdS/CFT

AdS/CFT
Name	AdS/CFT correspondence
Field	Theoretical physics
Introduced	1997
Authors	Juan Martín Maldacena
Institutions	Institute for Advanced Study

AdS/CFT The AdS/CFT correspondence is a conjectured duality linking gravity in anti–de Sitter spacetime with conformal field theories on its boundary. It proposes an equivalence between string theory or quantum gravity in a bulk spacetime and a lower-dimensional quantum field theory without gravity, reshaping approaches to Juan Martín Maldacena, Edward Witten, Joseph Polchinski, Gerard 't Hooft, and Leonard Susskind research programs. The correspondence has influenced work at Institute for Advanced Study, Princeton University, Harvard University, Massachusetts Institute of Technology, and Institute for Theoretical Physics (Amsterdam).

Introduction

The correspondence arose from attempts to reconcile results from String theory, Supergravity, and Quantum field theory with insights from Black hole thermodynamics, Hawking radiation, Bekenstein–Hawking entropy, and the Information paradox. Maldacena's proposal produced links among Type IIB string theory, N = 4 supersymmetric Yang–Mills theory, Anti-de Sitter space, Conformal field theory, and notions developed by Gerard 't Hooft such as the Holographic principle. Early reactions involved figures at CERN, Caltech, Stanford University, Perimeter Institute, Max Planck Institute for Gravitational Physics, and Kavli Institute for Theoretical Physics.

Historical development and origins

Origins trace through the study of D-brane dynamics by Joseph Polchinski and the analysis of black branes by G. T. Horowitz and Andy Strominger. Precedents include t Hooft paper insights and Susskind's holographic ideas, alongside breakthroughs at SLAC, Brookhaven National Laboratory, and Los Alamos National Laboratory. Key events featured presentations at Strings 1997, seminars at Institute for Advanced Study, and follow-up papers by Edward Witten, Stephen Hawking, Kip Thorne, and Roger Penrose exploring causal structure in Anti-de Sitter space. Subsequent development involved collaborations with researchers from Columbia University, Yale University, University of California, Berkeley, University of Cambridge, Oxford University, Imperial College London, and University of Tokyo.

Statement of the correspondence

Roughly stated, the duality identifies quantum gravity or String theory on (d+1)-dimensional Anti-de Sitter space with a d-dimensional Conformal field theory such as N = 4 supersymmetric Yang–Mills theory with gauge group SU(N). Precise formulations relate partition functions and correlation functions following recipes proposed by Edward Witten and elaborated by Gubser, Klebanov, Polyakov; these build on techniques from Renormalization group studies by Kenneth Wilson and operator-state mapping reminiscent of Radial quantization used by Alexander Polyakov. Gauge/gravity dualities connect observables like Wilson loops introduced by Kenneth Wilson and stress tensors studied by Paul Dirac and Julian Schwinger.

Examples and explicit dualities

The canonical example matches Type IIB string theory on AdS5 × S5 with N = 4 supersymmetric Yang–Mills theory in four dimensions; this example traces to Maldacena and was elaborated by S. S. Gubser, Igor Klebanov, and Alexander Polyakov. Other explicit dualities include correspondences between M-theory on AdS4 × S7 and the ABJM theory developed by Ofer Aharony, Oded Bergman, Daniel Jafferis, and Juan Maldacena; and proposals connecting AdS3 × S3 × T4 to two-dimensional conformal field theorys studied by Cumrun Vafa and Edward Witten. Extensions involve Nonrelativistic holography with researchers at Duke University and University of Illinois Urbana-Champaign, and instances tying Higher spin gravity by Mikhail Vasiliev to vector models proposed by I. R. Klebanov and Alexander Polyakov.

Evidence and checks

Checks include matching of spectra between supergravity modes computed by Peter van Nieuwenhuizen and operator dimensions in N = 4 supersymmetric Yang–Mills theory analyzed by Erick Weinberg and Stephen Coleman. Calculations of correlation functions followed Witten’s prescription and were compared with perturbative computations by groups at Princeton University and Institute for Advanced Study. Thermodynamic matches involve Hawking–Page transition analyses by Stephen Hawking and Don Page, and entropy comparisons rooted in Bekenstein–Hawking entropy work. Nonperturbative evidence arises from studies of integrability by Niklas Beisert, Gleb Arutyunov, and Matthias Staudacher and tests from lattice-inspired approaches at CERN and KEK.

Applications and implications

Applications span condensed matter-inspired approaches at Stanford University and University of British Columbia, modeling of Quark–gluon plasma observed at Relativistic Heavy Ion Collider and Large Hadron Collider with inputs from PHENIX Collaboration and ALICE Collaboration, and explorations of quantum information concepts like Entanglement entropy influenced by Ryu–Takayanagi and Mark Van Raamsdonk proposals. The correspondence impacted studies of Superconductivity analogues by Subir Sachdev and Sean Hartnoll, and influenced mathematical physics at Institute des Hautes Études Scientifiques and Mathematical Sciences Research Institute. Philosophical and foundational implications were discussed at conferences organized by Perimeter Institute and Santa Fe Institute.

Mathematical structure and extensions

Mathematical structures involve representation theory developed by Pierre Deligne, algebraic geometry tied to work at Institut Fourier, and category-theoretic frameworks influenced by Maxim Kontsevich and Edward Witten. Extensions include holographic renormalization developed in collaborations involving Kostas Skenderis, higher-spin holography by Mikhail Vasiliev, and topological string variants related to Edward Witten's topological quantum field theory. Broader links connect to modularity studied by Don Zagier, index theorems by Atiyah–Singer, and geometric analysis influenced by Richard Schoen and Shing-Tung Yau.

Category:Theoretical physics