A universal feature of CFT Renyi entropy

TL;DR

This paper demonstrates a universal property of Renyi entropy in conformal field theories, showing the first correction near q=1 is proportional to the stress tensor two-point function coefficient C_T, applicable across all CFTs.

Contribution

It establishes a universal relation between the first correction of Renyi entropy near q=1 and the stress tensor two-point function coefficient C_T in any d-dimensional CFT.

Findings

The first correction to entanglement entropy near q=1 is proportional to C_T.

The result is supported by gravity and field theory computations.

Application to 3d vector models at large N confirms the universality.

Abstract

We show that for a d-dimensional CFT in flat space, the Renyi entropy S_q across a spherical entangling surface has the following property: in an expansion around q=1, the first correction to the entanglement entropy is proportional to C_T, the coefficient of the stress tensor vacuum two-point function, with a fixed d-dependent coefficient. This is equivalent to a similar statement about the free energy of CFTs living on S^1 x H^{d-1} with inverse temperature \beta=2\pi q. In addition to furnishing a direct argument applicable to all CFTs, we exhibit this result using a handful of gravity and field theory computations. Knowledge of C_T thus doubles as knowledge of Renyi entropies in the neighborhood of q=1, which we use to establish new results in 3d vector models at large N.