Universal relation between thermal entropy and entanglement entropy in CFT

TL;DR

This paper proves a universal relation between thermal entropy and entanglement entropy in 2D conformal field theories, including both discrete and continuous spectrum cases, using holographic and regularization methods.

Contribution

It provides a rigorous proof of the relation between thermal and entanglement entropy in 2D CFTs and extends the understanding to noncompact free scalar theories.

Findings

Proved the entropy relation for 2D CFT with discrete spectrum.

Extended the relation to noncompact free scalar after regularization.

Confirmed the holographic computation matches field theory results.

Abstract

Inspired by the holographic computation of large interval entanglement entropy of two dimensional conformal field theory at high temperature, it was proposed that the thermal entropy is related to the entanglement entropy as $S_{th}=\displaystyle{\lim_{l \to 0}(S_{EE}(R-l)-S_{EE}(l))}$. In this letter, we prove this relation for 2D CFT with discrete spectrum in two different ways. Moreover we discuss this relation for a 2D noncompact free scalar, which is a gapless CFT with continuous spectrum. We show that it could be recovered, after appropriately regularizing the theory.