Introduction to AdS-CFT

Abstract

These lectures present an introduction to AdS-CFT, and are intended both for begining and more advanced graduate students, which are familiar with quantum field theory and have a working knowledge of their basic methods. Familiarity with supersymmetry, general relativity and string theory is helpful, but not necessary, as the course intends to be as self-contained as possible. I will introduce the needed elements of field and gauge theory, general relativity, supersymmetry, supergravity, strings and conformal field theory. Then I describe the basic AdS-CFT scenario, of $\mathcal{N}=4$ Super Yang-Mills's relation to string theory in $Ad{S}_5\times S_5$, and applications that can be derived from it: 3-point functions, quark-antiquark potential, finite temperature and scattering processes, the pp wave correspondence and spin chains. I also describe some general properties of gravity duals of gauge theories.

133 pages, 13 figures; typos corrected, references added

References in corpus (31)

• Large N Field Theories, String Theory and Gravity
• Dirichlet-Branes and Ramond-Ramond Charges
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Wilson loops in large N field theories
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity
• Gluon scattering amplitudes at strong coupling
• Hard Scattering and Gauge/String Duality
• Correlation functions in the CFT(d)/AdS(d+1) correpondence
• String Solitons
• Towards the large N limit of pure N=1 super Yang Mills
• Penrose limits and maximal supersymmetry
• The String Dual of a Confining Four-Dimensional Gauge Theory
• Harmonic superpositions of M-branes
• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection
• Supersymmetric Gauge Theories and the AdS/CFT Correspondence
• Introduction to S-Duality in N=2 Supersymmetric Gauge Theory. (A pedagogical review of the work of Seiberg and Witten)
• Consistent nonlinear KK reduction of 11d supergravity on $Ad{S}_7\times S_4$ and self-duality in odd dimensions
• Consistency of the $Ad{S}_7\times S_4$ reduction and the origin of self-duality in odd dimensions
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Conformal Field Theory Correlators from Classical Scalar Field Theory on $Ad{S}_{d+1}$
• Spinning strings and integrable spin chains in the AdS/CFT correspondence
• The supergravity dual of a theory with dynamical supersymmetry breaking
• Lectures on the Plane-Wave String/Gauge Theory Duality
• High energy QCD scattering, the shape of gravity on an IR brane, and the Froissart bound
• Semiclassical Bethe Ansatz and AdS/CFT
• High energy QCD from Planckian scattering in AdS and the Froissart bound
• Heisenberg saturation of the Froissart bound from AdS-CFT
• Solitons, monopoles and duality: from sine-Gordon to Seiberg-Witten
• Classical AdS Superstring Mechanics
• Classical Geometry of De Sitter Spacetime : An Introductory Review

Cited by in corpus (33)

• Fluid dynamics of R-charged black holes
• n-ary algebras: a review with applications
• Holographic tensor network models and quantum error correction: A topical review
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography
• A Practical Mini-Course on Applied Holography
• Nucleon mass radii and distribution: Holographic QCD, Lattice QCD and GlueX data
• M2-branes and AdS/CFT
• STU/QCD Correspondence
• Quenched mesonic spectrum at large N
• Continuum-Mediated Self-Interacting Dark Matter
• A defect in holographic interpretations of tensor networks
• Experimental Search for Quantum Gravity
• Harmonic Superspace from the $Ad{S}_5\times S^5$ Pure Spinor Formalism
• Effective Field Theory in AdS: Continuum Regime, Soft Bombs, and IR Emergence
• $Ad{S}_5$ black hole at N=2 supergravity
• Quantization via Linear homotopy types
• Numerical relativity in higher dimensions
• Baryon Binding Energy in Sakai-Sugimoto Model
• Anisotropic Lifshitz holography in Einstein-Proca theory with stable negative mass spectrum
• Remarks on confinement driven by axion-like particles in Yang-Mills theories
• Pre-potential in the $Ad{S}_5\times S^5$ Type IIB superspace
• Energy loss and jet quenching parameter in a thermal non-relativistic, non-commutative Yang-Mills plasma
• Twistors, strings and supersymmetric gauge theories
• Comments on the T-dual of the gravity dual of D5-branes on $S^3$
• Quantum Black Holes
• The Firewall Paradox
• Relativistic fluid dynamics in heavy ion collisions
• Parton picture for the strongly coupled SYM plasma
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Matrix Model Maps and Reconstruction of AdS SUGRA Interactions
• Modave Lectures on Quantum Information: An Introduction to Channels and Applications to Black Holes and AdS/CFT
• Energy Momentum Tensor Correlators in Improved Holographic QCD
• Toroidal AdS Charged Branes and Toda Equations