Supersymmetric Gauge Theories and the AdS/CFT Correspondence

Abstract

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.

arXiv commentParagraph with (10.39) revised, refs. added, typos fixed; 145 pages; 14 figures; email to D.Z Freedman <[email protected]>

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• AdS/CFT Correspondence and Symmetry Breaking
• Modeling the fifth dimension with scalars and gravity
• Solutions Of Four-Dimensional Field Theories Via M Theory
• Correlation functions in the CFT(d)/AdS(d+1) correpondence
• Holographic Renormalization
• On the Holographic Renormalization Group
• Conformal Four Point Functions and the Operator Product Expansion
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• Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
• The String Dual of a Confining Four-Dimensional Gauge Theory
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• Holographic Probes of Anti-de Sitter Spacetimes
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• Graviton exchange and complete 4-point functions in the AdS/CFT correspondence
• The Coulomb Branch of Gauge Theory from Rotating Branes
• Spacetime and the Holographic Renormalization Group
• Positivity Constraints on Anomalies in Supersymmetric Gauge Theories
• Conformal Field Theory Correlators from Classical Field Theory on Anti-de Sitter Space II. Vector and Spinor Fields
• New Vacua of Gauged N=8 Supergravity
• Les Houches Lectures on De Sitter Space
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• Field Theory Tests for Correlators in the AdS/CFT Correspondence
• AdS/CFT 4-point functions: How to succeed at z-integrals without really trying
• On Four-point Functions in the CFT/AdS Correspondence
• Conformal Field Theory Correlators from Classical Scalar Field Theory on $Ad{S}_{d+1}$
• Instantons in supersymmetric Yang-Mills and D-instantons in IIB superstring theory
• Extremal Correlators in the AdS/CFT Correspondence
• Multiple-Trace Operators and Non-Local String Theories
• Operator Product Expansion of the Lowest Weight CPOs in N=4 SYM_4 at Strong Coupling
• On N=8 Supergravity on $Ad{S}_5$ and N=4 Superconformal Yang-Mills theory
• On the construction of local fields in the bulk of AdS_5 and other spaces
• The Operator Product Expansion of N=4 SYM and the 4-point Functions of Supergravity
• Four-point Functions of Lowest Weight CPOs in N=4 SYM_4 in Supergravity Approximation
• Nilpotent invariants in N=4 SYM
• TASI lectures on the Holographic Principle
• 4D Doubleton Conformal Theories, CPT and IIB String on AdS_5 X S^5
• General Scalar Exchange in AdS_d+1
• Scattering in Anti-de Sitter Space and Operator Product Expansion
• Gauge Boson Exchange in $Ad{S}_{d+1}$
• Supersymmetries and BPS Configurations on Anti-de Sitter Space
• K-K excitations on AdS_5 x S^5 as N=4 ``primary'' superfields
• A Critical Behaviour of Anomalous Currents, Electric-Magnetic Universality and CFT_4
• M Theory on AdS_p x S^{11-p} and Superconformal Field Theories
• Correlation Functions of the Energy Momentum Tensor on Spaces of Constant Curvature
• Extremal correlators in four-dimensional SCFT
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• Quarter BPS Operators in N=4 SYM
• On Non-renormalization and OPE in Superconformal Field Theories
• Two-point functions of chiral operators in {\cal N}=4 SYM at order g^4
• Scalar Quartic Couplings in Type IIB Supergravity on $Ad{S}_5\times S^5$
• On the OPE of 1/2 BPS Short Operators in N=4 SCFT${}_4$
• Correlation Functions of Operators and Wilson Surfaces in the d=6, (0,2) Theory in the Large N Limit
• Quantum Scalar Fields on Anti-de Sitter Spacetime
• A proof of the irreversibility of renormalization group flows in four dimensions
• AdS_5/CFT_4 Four-point Functions of Chiral Primary Operators: Cubic Vertices
• Anatomy of Two Holographic Renormalization Group Flows
• Near-extremal correlators and vanishing supergravity couplings in AdS/CFT
• On the correspondence between gravity fields and CFT operators
• Dilaton - fixed scalar correlators and AdS_5 x S^5 - SYM correspondence
• The large $N_c$ limit of four-point functions in N=4 super-Yang-Mills theory from anti-de Sitter Supergravity
• Non-renormalization of next-to-extremal correlators in N=4 SYM and the AdS/CFT correspondence
• Massive symmetric tensor field on AdS
• Universal properties of superconformal OPEs for 1/2 BPS operators in $3\le D\le 6$
• String corrections to four point functions in the AdS/CFT correspondence
• Matching Conditions and Duality in N=1 SUSY Gauge Theories in the Conformal Window
• Order 1/N^2 test of the Maldacena conjecture: Cancellation of the one-loop Weyl anomaly
• Correlation Functions in Holographic Renormalization Group Flows
• Exact Consequences of the Trace Anomaly in Four Dimensions
• Near-Extremal Correlators and Generalized Consistent Truncation for AdS_{4|7}\times S^{7|4}
• A note on gravity-scalar fluctuations in holographic RG flow geometries
• Killing spinors and Supersymmetry on AdS
• Brane-world Kaluza-Klein reductions and Branes on the Brane
• CFT/CFT interpolating RG flows and the holographic c-function
• The Kahler Structure of Supersymmetric Holographic RG Flows
• An N=1 Supersymmetric Coulomb Flow
• Regular and Irregular Boundary Conditions in the AdS/CFT Correspondence
• Interacting singletons
• (2,0) Superconformal OPEs in D=6, Selection Rules and Non-renormalization Theorems
• Conformal partial wave analysis of AdS amplitudes for dilaton-axion four-point functions
• Current correlators in the Coulomb branch of N=4 SYM
• Superconformal 6D (2,0) theories in superspace
• Instantons and Non-renormalisation in AdS/CFT
• (Non-)perturbative tests of the AdS/CFT correspondence
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• Holographic Renormalization Group with Fermions and Form Fields
• Representations of superconformal algebras in the AdS_7/4/CFT_6/3 correspondence
• Dual expansions of N=4 super Yang-Mills theory via IIB superstring theory
• A Regularization Scheme for the AdS/CFT Correspondence
• AdS/CFT correspondence for n-point functions
• The antisymmetric tensor propagator in AdS
• Instantons and scattering in N=4 SYM in 4D
• AdS Box Graphs, Unitarity and Operator Product Expansions
• AdS Dynamics for Massive Scalar Field: exact solutions vs. bulk-boundary propagator
• The AdS-CFT correspondence, consistent truncations and gauge invariance

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