TASI Lectures: Introduction to the AdS/CFT Correspondence

By I. Klebanov. 2000

208 citations recorded by the source corpus.

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 solutions leads to dualities between conformal large $N$ gauge theories in 4 dimensions and string backgrounds of the form $AdS_5\times X_5$ where $X_5$ is an Einstein manifold. The gauge invariant chiral operators of the field theory are in one-to-one correspondence with the supergravity modes, and their correlation functions at strong `t Hooft coupling are determined by the dependence of the supergravity action on AdS boundary conditions. The simplest case is when $X_5$ is a 5-sphere and the dual gauge theory is the ${\cal N}=4$ supersymmetric SU(N) Yang-Mills theory. We also discuss D3-branes on the conifold corresponding to $X_5$ being a coset space $T^{1,1}=(SU(2)\times SU(2))/U(1)$. This background is dual to a certain ${\cal N}=1$ superconformal field theory with gauge group $SU(N)\times SU(N)$.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/aca501842975ab738391c9f42ac3cc2729fa89f7

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Citations in the corpus

Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts (2007, background): “A promising direction has been proposed by Maldacena [197] who proposed a connection between the strongly coupling limit of a conformal field theory (CFT) defined on the Anti-de-Sitter (AdS) asymptotic boundary [198,199], and the propagation of weakly coupled strings in a higher dimensional AdS spac”
Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality (2012, background): “Anti de-Sitter space The anti-de Sitter space is a maximally symmetric, homogeneous and isotropic space-time with constant negative curvature (hyperboloid) [82, 83, 84].”
Light-front holographic QCD and emerging confinement (2014, background): “relevant to other areas. Anumber ofexcellent reviews ontheAdS/CFT correspondence arealreadyavailable. We refer the reader to the Physics Report by Aharony, et al. [131], the TASI lectures by Klebanov [132] and by D’Hoker and Freedman [133] for some early reviews. For more recent discussions of holog”
A Universal result on central charges in the presence of double trace deformations (2002, unknown): “There exist many checks of the duality based on studying explicit models; the most extensively studied one is the N = 4 SYM theory dual to type IIB string theory in AdS5 × S(5) (for reviews, see [4, 5, 6]).”
Semiclassical Strings and AdS/CFT (2004, background): “To check the relation E = ∆ is then a non-trivial problem, except in the case of 1/2 BPS (single-trace chiral primary) operators which are dual to the supergravity states when the energies/dimensions are protected from corrections [4] and thus can be matched on the symmetry grounds.”
On D3-brane Potentials in Compactifications with Fluxes and Wrapped D-branes (2006, methodology): “Hence, it is possible, and convenient, to use methods and perspectives from the AdS/CFT correspondence [24] (see [25, 26] for reviews).”
Momentum fluctuations of heavy quarks in the gauge-string duality (2006, methodology): “The venue for the string theory calculations is the gauge-string duality [24, 25, 26] (for reviews see [27, 28, 29]), in particular the computation of Wilson loops through dual classical configurations of fundamental strings in anti-de Sitter space, as first considered in [30, 31].”
Heavy ions and string theory (2013, methodology): “Calculations of real-time processes remained difficult to address even in the large-Nc context until a fundamental breakthrough took place in 1997, with the formulation of the AdS/CFT, or gauge/gravity, correspondence [2, 3, 4]; for reviews see for example [5, 6, 7, 8].”
Entropy current in conformal hydrodynamics (2008, background): “This duality is called the AdS/CFT correspondence(See [8, 9, 10] for a review).”
Liouville Field Theory — A decade after the revolution (2004, background): “Since this realm is so vast, we refer to other excellent reviews [68], [69], lecture notes (to name a few [70], [71], [72]) or original papers [73], [74], [75] on this subject for details.”