Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT

Abstract

We calculate the contributions of a general non-vacuum conformal family to Rényi entropy in two-dimensional conformal field theory (CFT). The primary operator of the conformal family can be either non-chiral or chiral, and we denote its scaling dimension by $\Delta$. For the case of two short intervals on complex plane, we expand the Rényi mutual information by the cross ratio $x$ to order $x^{2\Delta +2}$. For the case of one interval on torus with the temperature being low, we expand the Rényi entropy by $q=\exp (-2\pi \beta /L)$, with $\beta$ being the inverse temperature and $L$ being the spatial period, to order $q^{\Delta +2}$. To make the result meaningful, we require that the scaling dimension $\Delta$ cannot be too small. For two intervals on complex plane we need $\Delta >1$, and for one interval on torus we need $\Delta >2$. We work in small Newton constant limit in gravity side and so large central charge limit in CFT side, and find matches of gravity and CFT results.

V1, 14 pages; V2, 15 pages, typos corrected, published version

References in corpus (12)

• Entanglement entropy of two disjoint intervals in conformal field theory II
• Entanglement Entropy at Large Central Charge
• Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy
• 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
• Short interval expansion of Rényi entropy on torus
• Universal relation between thermal entropy and entanglement entropy in CFT
• On one-loop entanglement entropy of two short intervals from OPE of twist operators
• Higher Spin Entanglement Entropy
• Higher spin entanglement entropy at finite temperature with chemical potential
• Holographic Rényi entropy for two-dimensional $\mathcal{N}$=(2,2) superconformal field theory

Cited by in corpus (2)

• Holographic Rényi entropy for two-dimensional $\mathcal{N}$=(2,2) superconformal field theory
• Subsystem fidelity in two-dimensional conformal field theories