Twist operators in higher dimensions

TL;DR

The paper develops a universal framework for twist operators in higher-dimensional CFTs by exploiting the replica trick and mapping entangling-sphere problems to thermal physics on $S^1\times H^{d-1}$, expressing the twist conformal dimension $h_n$ in terms of energy densities. It proves that the first derivative $\partial_n h_n|_{n=1}$ is universal and fixed by the stress-tensor two-point function via $C_T$, while the second derivative $\partial_n^2 h_n|_{n=1}$ is determined by three-point stress-tensor data $(\hat a,\hat b,\hat c)$, with higher derivatives tied to higher-point correlators. The results are validated through holographic models and free-field calculations, and connections to the Rényi entropy expansion (as in Perlmutter) are established, including OPE analyses of spherical twist operators and modular-Hamiltonian representations. Altogether, the work unifies twist-operator data across general CFTs in dimensions above two and provides robust tools for studying entanglement-related observables in higher dimensions.

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.