Thermal corrections to Rényi entropies for free fermions

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 2θ. 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.