Thermal Corrections to Rényi entropies for Free Fermions

Abstract

We calculate thermal corrections to Rényi entropies for free massless fermions on a sphere. More specifically, we take a free fermion on $\mathbb{R}\times {\mathbb{S}}^{d-1}$ and calculate the leading thermal correction to the Rényi entropies for a cap like region with opening angle $2\theta$. By expanding the density matrix in a Boltzmann sum, the problem of finding the Rényi entropies can be mapped to the problem of calculating a two point function on an $n$ sheeted cover of the sphere. We follow previous work for conformal field theories to map the problem on the sphere to a conical region in Euclidean space. By using the method of images, we calculate the two point function and recover the Rényi entropies.

15 pages, 5 figures