Conformal perturbation theory, dimensional regularization and AdS/CFT

Abstract

We study relevant deformations of conformal field theory on a cylinder using conformal perturbation theory, and in particular the one point function of the deformation operator and the energy in a system after a quench. We do the one point function calculation in both AdS and the conformal field theory and we show that the results match. Our calculations are done with arbitrary spacetime dimension, as well as arbitrary scaling dimension of the relevant operator. The only singularities that appear in the end calculation can be related to logarithmic singularities in dimensional regularization. We also study time dependent setups in the field theory and we show how the response of the system can be calculated in a Hamiltonian based approach. We use this procedure to explain certain short time universal results that have been found previously.

18 pages

References in corpus (10)

• Gauge Theory Correlators from Non-Critical String Theory
• AdS/CFT Correspondence and Symmetry Breaking
• Correlation functions in the CFT(d)/AdS(d+1) correpondence
• Holographic Renormalization
• The Operator Product Expansion for Wilson Loops and Surfaces in the Large N Limit
• Quantum quenches of holographic plasmas
• Thermal quenches in N=2* plasmas
• Universal scaling in fast quantum quenches in conformal field theories
• States and Boundary Terms: Subtleties of Lorentzian AdS/CFT
• Universality of Abrupt Holographic Quenches

Cited by in corpus (25)

• Entanglement Growth after a Global Quench in Free Scalar Field Theory
• Nonlocal probes of thermalization in holographic quenches with spectral methods
• Smooth and fast versus instantaneous quenches in quantum field theory
• Lifting of D1-D5-P states
• On Higher-Spin Points and Infinite Distances in Conformal Manifolds
• Quantum Field Theory, Feynman-, Wheeler Propagators, Dimensional Regularization in Configuration Space and Convolution of Lorentz Invariant Tempered Distributions
• Lifting at higher levels in the D1D5 CFT
• Lifting of level-1 states in the D1D5 CFT
• Conformal Perturbation Theory for Twisted Fields
• ISCOs in AdS/CFT
• Entanglement entropy of excited states in conformal perturbation theory and the Einstein equation
• Lifting of states in 2-dimensional $N=4$ supersymmetric CFTs
• Aspects of thermal one-point functions and response functions in AdS Black holes
• Dimensionally regularized Tsallis' Statistical Mechanics and two-body Newton's gravitation
• Localized states in global AdS
• Dimensionally regularized Boltzmann-Gibbs Statistical Mechanics and two-body Newton's gravitation
• First-order conformal perturbation theory by marginal operators
• Universality of fast quenches from the conformal perturbation theory
• Newton's gravitation-force's classical average proof of a Verlinde's conjecture
• Dynamical evolution in the D1D5 CFT
• Aspects of Holography in Conical $Ad{S}_3$
• Quenches on thermofield double states and time reversal symmetry
• Spinning Particle Geometries in AdS${}_3$/CFT${}_2$
• Entanglement Entropy with a Time-dependent Hamiltonian
• Comments on contact terms and conformal manifolds in the AdS/CFT correspondence