Supersymmetric gauge theories and the AdS / CFT correspondence

By E. D’Hoker, D. Freedman. 2002

738 citations recorded by the source corpus.

In these lecture notes we first assemble the basic ingredients of supersymmetric gauge theories (particularly N=4 super-Yang-Mills theory), supergravity, and superstring theory. Brane solutions are surveyed. The geometry and symmetries of anti-de Sitter space are discussed. The AdS/CFT correspondence of Maldacena and its application to correlation functions in the the conformal phase of N=4 SYM are explained in considerable detail. A pedagogical treatment of holographic RG flows is given including a review of the conformal anomaly in four-dimensional quantum field theory and its calculation from five-dimensional gravity. Problem sets and exercises await the reader.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/7fe97fd75e9b0c0ef3a3d25d0c5766cd2ba24c4b

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In Astronomy and Astrophysics

1. V. Hubeny
2. M. Rangamani
3. S. Hartnoll
4. S. Gubser
5. S. Sachdev
6. A. Tseytlin
7. R. Myers
8. T. Takayanagi

In Nuclear and High Energy Physics

1. A. Tseytlin
2. N. Beisert
3. S. Frolov
4. J. Maldacena
5. R. Roiban
6. G. Arutyunov
7. M. Rangamani
8. V. Hubeny

Citations in the corpus

• Quantum critical transport, duality, and M-theory (2007, background): “The weak- coupling action and field content of this theory is most directly understood by dimensional reduction of the N = 1 SYM theory in D = 9+1 on the flat torus T 7 [62].”
• The fluid/gravity correspondence: a new perspective on the membrane paradigm (2010, neutral): “3 The AdS/CFT correspondence is comprehensively reviewed in the classic reviews [29, 30].”
• Exact half-BPS Type IIB interface solutions. I. Local solution and supersymmetric Janus (2007, methodology): “rsymmetric Janus doped with D5 and/or NS5 branes, is deferred to a companion paper [1]. 1 Introduction A particularly interesting application of the AdS/CFT correspondence [2, 3, 4] (for reviews, see [5, 6]) is provided by conformal field theory (CFT) in the presence of a planar interface or a planar”
• Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality (2012, methodology): “In the original version of the mapping the quantum field theory is a QCD-like theory known as N = 4 supersymmetric (SUSY) Yang-Mills theory [230].”
• Holographic Duality with a View Toward Many-Body Physics (2009, background): “Material from other review articles, including [1, 3, 4, 2, 5, 6, 7], has been liberally borrowed to construct these notes.”
• AdS dual of the critical O(N) vector model (2002, methodology): “In AdS calculations of 4-point functions of 1-particle operators, the logarithmic terms of the type described above were found in [34, 35].”
• Interface Yang–Mills, supersymmetry, and Janus (2006, background): “The Janus solutions offer interesting candidates for further exploring the AdS/CFT correspondence [5, 6, 7] (for reviews, see [ 8 , 9]).”
• 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.”
• On Higher Spin Gauge Theory and the Critical O(N) Model (2011, background): “In perturbation theory, the boundary condition affects correlation functions only through a modification of the bulk scalar propagator [20, 21],(5) G∆(x, x ) = 1 4π2 ξ 1− ξ2 , ξ = 1 cosh d(x, x′) , (4.”
• Lessons from the information paradox (2020, background): “er on perturbation theory in global AdS In this section, we provide a very quick review of the behaviour of perturbative elds in global AdS. Many existing and excellent reviews of perturbation theory [243,244] tend to focus on Poincare AdS, which provides a technically simpler arena for the computat”
• A Universal result on central charges in the presence of double trace deformations (2002, neutral): “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 (for reviews, see [4, 5, 6]).”