Twist operators in higher dimensions

TL;DR

This paper investigates higher-dimensional twist operators in conformal field theories, expressing their conformal dimensions via energy density, expanding around n=1, and validating results through holography and free field theory.

Contribution

It introduces a power series expansion of twist operator dimensions around n=1 and relates coefficients to energy-momentum tensor correlations, with universal first and second derivatives.

Findings

Agreement between holography and free field theory results

Universal form of first and second derivatives of conformal dimensions

Insights into operator product expansion of spherical twist operators

Abstract

We study twist operators in higher dimensional CFT's. In particular, we express their conformal dimension in terms of the energy density for the CFT in a particular thermal ensemble. We construct an expansion of the conformal dimension in power series around n=1, with n being replica parameter. We show that the coefficients in this expansion are determined by higher point correlations of the energy-momentum tensor. In particular, the first and second terms, i.e. the first and second derivatives of the scaling dimension, have a simple universal form. We test these results using holography and free field theory computations, finding agreement in both cases. We also consider the `operator product expansion' of spherical twist operators and finally, we examine the behaviour of correlators of twist operators with other operators in the limit n ->1.