Exact results for corner contributions to the entanglement entropy and Renyi entropies of free bosons and fermions in 3d

Abstract

In the presence of a sharp corner in the boundary of the entanglement region, the entanglement entropy (EE) and Renyi entropies for 3d CFTs have a logarithmic term whose coefficient, the corner function, is scheme-independent. In the limit where the corner becomes smooth, the corner function vanishes quadratically with coefficient $\sigma$ for the EE and ${\sigma }_n$ for the Renyi entropies. For a free real scalar and a free Dirac fermion, we evaluate analytically the integral expressions of Casini, Huerta, and Leitao to derive exact results for $\sigma$ and ${\sigma }_n$ for all $n=2,3,\dots$. The results for $\sigma$ agree with a recent universality conjecture of Bueno, Myers, and Witczak-Krempa that $\sigma /C_T={\pi }^2/24$ in all 3d CFTs, where $C_T$ is the central charge. For the Renyi entropies, the ratios ${\sigma }_n/C_T$ do not indicate similar universality. However, in the limit $n\to \infty$, the asymptotic values satisfy a simple relationship and equal $1/(4{\pi }^2)$ times the asymptotic values of the free energy of free scalars/fermions on the $n$-covered 3-sphere.

10 pages, 2 figures. v2: typos corrected, references added, asymptotics updated

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