Universal Thermal Corrections to Entanglement Entropy for Conformal Field Theories on Spheres

TL;DR

This paper derives a universal formula for the leading thermal correction to entanglement entropy in conformal field theories on spheres, validated by numerical calculations for a scalar field.

Contribution

It provides a universal expression for thermal corrections to entanglement entropy in CFTs on spheres, dependent only on the mass gap and geometric parameters.

Findings

Universal correction depends only on mass gap and geometry.

Numerical verification for a scalar field confirms the theoretical prediction.

Boundary term considerations resolve apparent discrepancies.

Abstract

We consider entanglement entropy of a cap-like region for a conformal field theory living on a sphere times a circle in d space-time dimensions. Assuming that the finite size of the system introduces a unique ground state with a nonzero mass gap, we calculate the leading correction to the entanglement entropy in a low temperature expansion. The correction has a universal form for any conformal field theory that depends only on the size of the mass gap, its degeneracy, and the angular size of the cap. We confirm our result by calculating the entanglement entropy of a conformally coupled scalar numerically. We argue that an apparent discrepancy for the scalar can be explained away through a careful treatment of boundary terms. In an appendix, to confirm the accuracy of the numerics, we study the mutual information of two cap-like regions at zero temperature.