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| Maldacena duality | |
|---|---|
| Name | Maldacena duality |
| Discoverer | Juan Maldacena |
| Year | 1997 |
| Field | String theory |
| Also known as | AdS/CFT correspondence |
Maldacena duality is a conjectured equivalence between certain quantum gravity theories in asymptotically anti‑de Sitter spacetimes and conformal field theorys defined on the boundary of those spacetimes, proposed in 1997 by Juan Maldacena. The proposal links models in string theory and M-theory with strongly coupled gauge theorys, and it has become a central tool in modern theoretical physics research, influencing studies in black hole thermodynamics, quantum information theory, and condensed matter physics.
Maldacena's 1997 conjecture arose in the context of prior work on D-brane dynamics, Type IIB superstring theory, and the study of near‑horizon geometries such as AdS5 × S5, drawing on results from Strominger–Vafa black hole entropy, Polchinski's D-branes, and earlier developments in supersymmetry and supergravity. The duality proposes a nontrivial relation between a gravitational theory in an anti-de Sitter space and a lower‑dimensional conformal field theory, connecting techniques from perturbative string theory, nonperturbative effects, and holographic principle ideas inspired by Gerard 't Hooft and Leonard Susskind.
The original precise example equates Type IIB string theory on AdS5 × S5 with four‑dimensional N=4 supersymmetric Yang–Mills theory with gauge group SU(N). In this setup the radial coordinate of AdS5 maps to the renormalization group scale of the conformal field theory, while the isometries of S5 correspond to the R-symmetry of the supersymmetric field theory; this mapping builds on symmetry correspondences used in analyses by Maldacena and elaborated by Gubser, Klebanov, Polyakov and Witten. Parameters relate via the 't Hooft coupling λ = g^2_{YM} N and the string coupling g_s, with large N and large λ corresponding to classical supergravity limits, echoing insights from ’t Hooft planar expansion.
Evidence for the conjecture includes matching of spectrum and correlation functions: classical supergravity mode spectra in AdS5 × S5 reproduce protected operator dimensions in N=4 supersymmetric Yang–Mills theory, verified using techniques developed by Witten (1998), Gubser–Klebanov–Polyakov (1998), and later perturbative checks by Minahan, Beisert, Staudacher, and others in the context of integrability. Thermodynamic comparisons match the entropy of large AdS black holes to the thermal entropy of strongly coupled gauge theory plasmas, with seminal contributions from Hawking, Page, Witten (1998 thermal), and studies of quark–gluon plasma phenomena inspired by RHIC and LHC experiments. Further checks arise from computations of Wilson loops via string worldsheet minimal surfaces following methods by Maldacena (1998 Wilson), and from protected quantities computed by localization techniques cross‑checked with holographic results by Pestun and collaborators.
The duality has been generalized to other dimensions and setups: examples include AdS3/CFT2 dualities connected to D1–D5 systems, relations to AdS4/CFT3 incarnations such as the ABJM theory in M-theory backgrounds, and proposals linking nonconformal brane systems to nonrelativistic holography and Lifshitz or Schrödinger geometries used in condensed matter analogies. Extensions incorporate backgrounds with less supersymmetry, orbifolds and orientifolds studied by Kachru, Silverstein, and Gukov, and top‑down versus bottom‑up model building surveyed in reviews by Klebanov, Polchinski, and Skenderis.
Maldacena duality has been applied to problems across high energy physics and beyond: modeling transport coefficients and viscosity bounds in strongly coupled plasmas inspired by Kovtun, Son, Starinets; exploring information paradox aspects via holographic entanglement entropy using the Ryu–Takayanagi prescription; studying quantum chaos and spectral statistics connected to Sachdev–Ye–Kitaev model analogies and insights from Hayden–Preskill and Almheiri–Marolf analyses; and providing tools for holographic approaches to condensed matter phenomena like superconductivity in holographic superconductor models developed by Gubser and Hartnoll. Holography also impacts mathematical physics subjects such as geometric representation theory considered by Witten (S-duality) and Kapustin.
Mathematical facets involve rigorous constructions of mapping between bulk and boundary operators, elucidation of quantum error‑correcting code structures in holography inspired by work of Almheiri, Dong, Harlow, and connections to integrability and spectral curves analyzed by Beisert, Arutyunov, and Zarembo. The holographic dictionary formalized by Witten and Gubser–Klebanov–Polyakov translates bulk action functionals into generating functionals of boundary correlators, and mathematicians have pursued formulations linking holography to aspects of Kähler geometry, Teichmüller theory, and categorical structures influenced by Kontsevich and Seiberg–Witten techniques.
Open problems include proving the duality beyond supersymmetric or large N limits, constructing precise duals for realistic cosmology such as de Sitter space pursued by Strominger (dS/CFT) and others, resolving the black hole interior and information recovery in dynamical settings studied by Penington and Almheiri et al. via island prescriptions, and extending holography to finite N nonperturbatively through bootstrap and lattice approaches explored by Rattazzi and Yamashita. Further directions probe relations to quantum gravity axioms, emergence of spacetime from entanglement as advocated by Van Raamsdonk, and potential experimental signatures in condensed matter systems and heavy‑ion collisions guided by collaborations among theorists at institutions like Institute for Advanced Study, Perimeter Institute, and CERN.