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| AdS_3/CFT_2 | |
|---|---|
| Name | AdS3/CFT2 |
| Subject | Theoretical physics |
| Field | String theory, Quantum field theory |
| Introduced | 1997 |
| Notable contributors | Juan Maldacena, Edward Witten, Andrew Strominger, Gary T. Horowitz, Cumrun Vafa |
AdS_3/CFT_2. AdS_3/CFT_2 is a specific instance of the holographic duality relating a three-dimensional anti-de Sitter spacetime to a two-dimensional conformal field theory, providing a nonperturbative map between String theory, Quantum gravity, Conformal field theory, and Statistical mechanics. The correspondence has been central to developments involving the BTZ black hole, Brown–Henneaux central charge, Virasoro algebra, and constructions in Type IIB string theory, shaping research agendas at institutions such as Institute for Advanced Study and Perimeter Institute for Theoretical Physics.
The origins of the correspondence trace to work by Juan Maldacena on the AdS/CFT correspondence and foundational methods by Edward Witten, Steven Gubser, Igor Klebanov, and Alexander Polyakov, connecting Anti-de Sitter space to Conformal field theory and influenced by earlier results from Brown–Henneaux and concepts from S-matrix theory. Developments involved collaborations among researchers at CERN, Harvard University, Caltech, Princeton University, and University of Cambridge, and leveraged techniques from Representation theory, Algebraic geometry, Modular forms, and Vertex operator algebra.
Three-dimensional anti-de Sitter space appears in analyses by Bañados, Teitelboim, and Zanelli whose discovery of the BTZ black hole and the Brown–Henneaux central charge illuminated how asymptotic symmetries yield a pair of Virasoro algebra copies; these results interface with work by Carlip on black hole entropy and by Strominger on microstate counting. Gravity in three dimensions simplifies relative to General relativity in four dimensions and connects to formulations such as Chern–Simons theory described by Witten (1988), while classical solutions and thermodynamics link to analyses from Hawking, Bekenstein, and Henneaux.
Two-dimensional conformal field theories underpin the dual side, with paradigmatic models like the Ising model, Wess–Zumino–Witten model, Liouville field theory, and minimal models studied by Belavin, Polyakov, and Zamolodchikov. Key structures involve the Virasoro algebra, the Kac–Moody algebra, modular invariance exploited in work by Cardy and Verlinde, and applications in Statistical mechanics and Condensed matter physics examined by groups at MIT, University of California, Berkeley, and Stanford University.
The holographic dictionary relates bulk fields in Anti-de Sitter space to boundary operators in Conformal field theory, with prescriptions developed by Gubser, Klebanov, and Polyakov and refined by Witten; central quantities include correlators, operator dimensions, and central charges derived via the Brown–Henneaux relation. Matching between bulk geodesics and boundary conformal blocks invokes work by Fitzpatrick, Kaplan, and Penedones and integrates techniques from Modular forms, Representation theory, and the S-matrix program.
The BTZ black hole provides a laboratory for black hole thermodynamics and microstate counting via boundary states explored by Strominger, Maldacena', and Seiberg; realizations in Type IIB string theory and M-theory involve brane constructions studied by Polchinski, Johnson, Myers, and Vafa, and relate to D1/D5 systems analyzed by Maldacena, Ooguri, and Strominger. Connections to Topologically massive gravity and proposals from Witten (2007) and Gaberdiel–Gopakumar extend examples to higher spin theories and to dualities with large-N symmetric orbifolds investigated by Dijkgraaf and Mathur.
Checks of the correspondence use computation of correlation functions via bulk perturbation theory per Witten and bootstrap methods per Rattazzi and Poland; entanglement entropy computations employ the Ryu–Takayanagi formula and its extensions by Hubeny, Rangamani, and Takayanagi with comparisons to CFT entanglement results from Calabrese and Cardy. Partition functions on torus and modular bootstrap techniques draw on work by Cardy, Verlinde, and Zamolodchikov, while perturbative expansions and 1/N analyses build on methods developed at SLAC National Accelerator Laboratory and CERN.
Active extensions include higher spin holography advanced by Gaberdiel and Gopakumar, nonrelativistic limits studied by Son and Balasubramanian, and relations to integrability explored by Beisert and Minahan. Open problems involve precise bulk reconstruction debated by Hamilton, Kabat, Lifschytz, and Lowe, understanding microstate structure following proposals by Mathur and Bena, and formulating a fully nonperturbative dual for general asymptotically AdS3 spacetimes pursued at Perimeter Institute for Theoretical Physics, KITP, and IAS.