Universal relation between thermal entropy and entanglement entropy in CFT

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 $S_{th}=\underset{l\to 0}{\lim }(S_{EE}(R-l)-S_{EE}(l))$. 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.

5 pages, 1 figure. Revised discussion on noncompact free scalar, match with published version

References in corpus (5)

• Entanglement Entropy at Large Central Charge
• Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
• The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT
• Universal Thermal Corrections to Single Interval Entanglement Entropy for Conformal Field Theories
• Single Interval Rényi Entropy At Low Temperature

Cited by in corpus (5)

• Rényi Entropy of Free Compact Boson on Torus
• Corrections to holographic entanglement plateau
• Rényi Entropy for a $2d$ CFT with a gauge field: $\widehat{\mathrm{SU}}(\mathbf{N}{)}_1$ WZW theory on a branched torus
• Modular invariance and entanglement entropy
• Long-range correlation of CMB temperature fluctuations from the holographic entanglement entropy