The AdS/CFT Correspondence: Classical, Quantum, and Thermodynamical Aspects

Abstract

Certain aspects of the AdS/CFT correspondence are studied in detail. We investigate the one-loop mass shift to certain two-impurity string states in light-cone string field theory on a plane wave background. We find that there exist logarithmic divergences in the sums over intermediate mode numbers which cancel between the cubic Hamiltonian and quartic "contact term". We argue that generically, every order in intermediate state impurities contributes to the mass shift at leading perturbative order. The same mass shift is also computed using an improved 3-string vertex proposed by Dobashi and Yoneya. The result is found to agree with gauge theory at leading order and is close but not quite in agreement at subleading order. We extend the analysis to include discrete light-cone quantization, considering states with up to three units of p+. We study the (apparently) first-order phase transition in the weakly coupled plane-wave matrix model at finite temperature. We analyze the effect of interactions by computing the relevant parts of the effective potential for the Polyakov loop operator to three loop order. We show that the phase transition is indeed of first order. We also compute the 2-loop correction to the Hagedorn temperature. Finally, correlation functions of 1/4 BPS Wilson loops with the infinite family of 1/2 BPS chiral primary operators are computed in N=4 super Yang-Mills theory by summing planar ladder diagrams. The correlation functions are also computed in the strong-coupling limit using string theory; the result is found to agree with the extrapolation of the planar ladders. The result is related to similar correlators of 1/2 BPS loops by a simple re-scaling of the coupling constant, discovered by Drukker for the case of the 1/4 BPS loop VEV.

PhD Thesis (supervisor: Gordon W. Semenoff), University of British Columbia, 190 pages, numerous figures. Section 2.5 contains some previously unpublished results for DLCQ plane-wave strings. Updated references in v2

References in corpus (70)

• M Theory As A Matrix Model: A Conjecture
• The Dynamics of General Relativity
• Wilson loops in large N field theories
• Dielectric-Branes
• String Solitons
• D-branes, Quivers, and ALE Instantons
• Wilson Loops in N=4 Supersymmetric Yang--Mills Theory
• An Exact Prediction of N=4 SUSYM Theory for String Theory
• Entropy and Temperature of Black 3-Branes
• Exactly solvable model of superstring in Ramond-Ramond plane wave background
• Wilson Loops and Minimal Surfaces
• The Operator Product Expansion for Wilson Loops and Surfaces in the Large N Limit
• Graviton exchange and complete 4-point functions in the AdS/CFT correspondence
• M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory
• String Theory and Classical Absorption by Threebranes
• A New Double-Scaling Limit of N=4 Super Yang-Mills Theory and PP-Wave Strings
• Another Conjecture about M(atrix) Theory
• Matrix Perturbation Theory For M-theory On a PP-Wave
• The wall of the cave
• Exact anomalous dimensions of {\cal N}=4 Yang-Mills operators with large R charge
• AdS/CFT 4-point functions: How to succeed at z-integrals without really trying
• On Four-point Functions in the CFT/AdS Correspondence
• Superstring Interactions in a pp-wave Background
• Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion
• Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions
• Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions
• Transverse Fivebranes in Matrix Theory
• Operator Mixing and the BMN Correspondence
• The Plane-Wave/Super Yang-Mills Duality
• Superstring Interactions in a pp-wave Background II
• Lectures on the Plane-Wave String/Gauge Theory Duality
• Can the effective string see higher partial waves?
• ADM masses for black strings and p-branes
• More comments on superstring interactions in the pp-wave background
• Strings from Quivers, Membranes from Moose
• Holographic Reformulation of String Theory on AdS_5 x S^5 background in the PP-wave limit
• Explicit Formulas for Neumann Coefficients in the Plane-Wave Geometry
• Resolving the Holography in the Plane-Wave Limit of AdS/CFT Correspondence
• The D-instanton and other supersymmetric D-branes in IIB plane-wave string theory
• AdS_5/CFT_4 Four-point Functions of Chiral Primary Operators: Cubic Vertices
• Wavy Wilson Line and AdS/CFT
• The 3-string vertex and the AdS/CFT duality in the PP-wave limit
• The large $N_c$ limit of four-point functions in N=4 super-Yang-Mills theory from anti-de Sitter Supergravity
• Fermionic Matrix Models
• On light-cone SFT contact terms in a plane wave
• String corrections to four point functions in the AdS/CFT correspondence
• SYM Description of PP-wave String Interactions: Singlet Sector and Arbitrary Impurities
• Comparing strings in AdS(5)xS(5) to planar diagrams: an example
• Five-Brane Thermodynamics from the Matrix Model
• Exact 1/4 BPS Loop - Chiral Primary Correlator
• Free Energy and Phase Transition of the Matrix Model on a Plane-Wave
• An alternative formulation of light-cone string field theory on the plane wave
• Properties of Chiral Wilson Loops
• Impurity Non-Preserving 3-Point Correlators of BMN Operators from PP-Wave Holography II : Fermionic Excitations
• Light-Cone String Field Theory in a Plane Wave Background
• Conformal partial wave analysis of AdS amplitudes for dilaton-axion four-point functions
• Two-Loop Partition Function in the Planar Plane-Wave Matrix Model
• Holographic cubic vertex in the pp-wave
• Exact Solution of the One-Dimensional Non-Abelian Coulomb Gas at Large N
• Strong Evidence In Favor OF The Existence Of S-Matrix For Strings In Plane Waves
• Superconformal Invariants or How to Relate Four-point AdS Amplitudes
• BMN operators with vector impurities, Z_2 symmetry and pp-waves
• Divergence Cancellation and Loop Corrections in String Field Theory on a Plane Wave Background
• New aspects of the BMN correspondence beyond the planar limit
• Non Perturbative Effects in QCD
• Calculation of Four Point Correlation Function of Logarithmic Conformal Field Theory Using AdS/CFT Correspondence
• Non-perturbative effects in the BMN limit of N=4 supersymmetric Yang-Mills
• Mixing of the RR and NSNS sectors in the BMN limit
• Towards S matrices on flat space and pp waves from SYM
• 1/2-BPS Correlators as c=1 S-matrix

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