# Anti-de Sitter space and holography

@article{Witten1998AntideSS,
title={Anti-de Sitter space and holography},
author={Edward Witten},
journal={Advances in Theoretical and Mathematical Physics},
year={1998},
volume={2},
pages={253-291}
}
• E. Witten
• Published 1998
• Physics
• Advances in Theoretical and Mathematical Physics
Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on… Expand
10,338 Citations

#### Figures from this paper

TASI Lectures: Introduction to the AdS/CFT Correspondence
This is an introductory review of the AdS/CFT correspondence and of the ideas that led to its formulation. We show how comparison of stacks of D3-branes with corresponding supergravity solutionsExpand
Quantum entropy and exact 4D/5D connection
A bstractWe consider the AdS2/CFT1 holographic correspondence near the horizon of rotating five-dimensional black holes preserving four supersymmetries in N=2$$\mathcal{N}=2$$ supergravity. TheExpand
D3-D7 holographic dual of a perturbed 3D CFT
• Physics
• 2013
An appropriately oriented D3-D7-brane system is the holographic dual of relativistic Fermions occupying a 2+1-dimensional defect embedded in 3+1-dimensional spacetime. The Fermions interact viaExpand
Holography and defect conformal field theories
• Physics
• 2002
We develop both the gravity and field theory sides of the Karch-Randall conjecture that the near-horizon description of a certain D5-D3 brane configuration in string theory, realized as AdS_5 x S^5Expand
Holography and Koszul duality: the example of the $M2$ brane
Si Li and author suggested in that, in some cases, the AdS/CFT correspondence can be formulated in terms of the algebraic operation of Koszul duality. In this paper this suggestion is checkedExpand
CFT/AdS correspondence, massive gravitons, and a connectivity index conjecture
• Physics
• 2006
We discuss the general question of which conformal field theories have dual descriptions in terms of quantum gravity theories on anti-de Sitter space. We analyze in detail the case of a deformedExpand
Superconformal Field Theory In Six Dimensions And Supertwistor
We studied the quantum dynamics of six dimensional $\mathcal{N}=(2, 0)$ superconformal field theory (the QNG theory). We developed the spinor technique for six-dimensional quantum field theories. ByExpand
Applications of the holographic principle in string theory
The holographic principle has become an extraordinary tool in theoretical physics, most notably in the form of the Anti-deSitter Conformal Field Theory (AdS/CFT ) correspondence, in which classicalExpand
• Physics, Mathematics
• 2020
We consider supergravity in five-dimensional Anti-De Sitter space $AdS_{5}$ with minimal supersymmetry, encoded by a Sasaki-Einstein metric on a five-dimensional compact manifold $M$. Our main resultExpand
Holography and compactification
Following a recent suggestion by Randall and Sundrum, we consider string compactification scenarios in which a compact slice of AdS-space arises as a subspace of the compactification manifold. AExpand

#### References

SHOWING 1-10 OF 95 REFERENCES
The Large-N Limit of Superconformal Field Theories and Supergravity
We show that the large-N limits of certainconformal field theories in various dimensions includein their Hilbert space a sector describing supergravityon the product of anti-de Sitter spacetimes,Expand
Gauge Theory Correlators from Non-Critical String Theory
• Physics
• 1998
Abstract We suggest a means of obtaining certain Green's functions in 3+1-dimensional N =4 supersymmetric Yang-Mills theory with a large number of colors via non-critical string theory. TheExpand
Stability in Gauged Extended Supergravity
• Physics
• 1982
Extended supergravity theories with gauged SO(N) internal symmetry have, for N ≥ 4, scalar field potentials which are unbounded below. Nevertheless, it is argued that the theories have ground statesExpand
Singletons, doubletons and M-theory
• Physics
• 1998
Abstract We identify the two-dimensional AdS subsupergroup OSp( 16 2 , R ) of the M-theory supergroup OSp( 1 32 , R ) which captures the dynamics of n DO-branes in the large n limit of Matrix theory.Expand
Macroscopic superstrings as interpolating solitons
• Physics
• 1994
Abstract It is known that, in string sigma-model metric, the ‘extreme’ fivebrane solution of D = 10 supergravity interpolates between D = 10 Minkowski spacetime and a supersymmetric S 3Expand
The background geometry of DLCQ supergravity
Abstract By following Seiberg's prescriptions on DLCQ of M theory, we give the background geometries of DLCQ supergravity associated with N sector of DLCQ of M theory on T p with vanishingly smallExpand
Spectrum of Large N Gauge Theory from Supergravity
• Physics
• 1998
Recently, Maldacena proposed that the large N limit of the N=4 supersymmetric gauge theory in four dimensions with U(N) gauge group is dual to the type IIB superstring theory on AdS_5 ×S^5. We useExpand
Supergravity and The Large N Limit of Theories With Sixteen Supercharges
• Physics
• 1998
We consider field theories with sixteen supersymmetries, which include U(N) Yang-Mills theories in various dimensions, and argue that their large N limit is related to certain supergravity solutions.Expand
Massless Particles, Conformal Group and De Sitter Universe
• Physics
• 1981
We first review a recent result on the uniqueness of the extension to the conformal group of massless representations of the Poincare group. By restricting these representations to SO(3,2) we obtainExpand
M theory as a matrix model: A Conjecture
• Physics
• 1997
We suggest and motivate a precise equivalence between uncompactified 11-dimensional M theory and the N={infinity} limit of the supersymmetric matrix quantum mechanics describing D0 branes. TheExpand