Conformal perturbation theory, dimensional regularization and AdS/CFT

TL;DR

This paper investigates relevant deformations of conformal field theories using conformal perturbation theory, comparing results from AdS and CFT calculations, and explores time-dependent responses and universal short-time behaviors.

Contribution

It provides a detailed analysis of relevant deformations in CFTs using conformal perturbation theory, matching AdS and CFT results across arbitrary dimensions and operator dimensions.

Findings

Matching results between AdS and CFT calculations for one-point functions.

Identification of logarithmic singularities related to dimensional regularization.

Explanation of universal short-time responses in time-dependent setups.

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.