On one-loop entanglement entropy of two short intervals from OPE of twist operators

TL;DR

This paper calculates the one-loop entanglement entropy for two short intervals in 2D CFT using twist operator OPE, focusing on stress tensor and higher spin contributions, and finds agreement with gravity results.

Contribution

It provides explicit calculations of one-loop entanglement entropy contributions from stress tensor and higher spin operators in 2D CFT, simplifying the process by focusing on the one-loop case.

Findings

Stress tensor contribution up to order x^{10}

W_3 operator contribution up to order x^{12}

W_4 operator contribution up to order x^{14}

Abstract

We investigate the one-loop entanglement entropy of two short intervals with small cross ratio $x$ on a complex plane in two-dimensional conformal field theory (CFT) using operator product expansion of twist operators. We focus on the one-loop entanglement entropy instead of the general order $n$ R\'enyi entropy, and this makes the calculation much easier. We consider the contributions of stress tensor to order $x^{10}$, contributions of $W_3$ operator to order $x^{12}$, and contributions of $W_4$ operator to order $x^{14}$. The CFT results agree with the ones in gravity.