A universal feature of charged entanglement entropy

TL;DR

This paper demonstrates a universal quadratic correction to charged entanglement entropy in higher-dimensional CFTs, governed by current correlators and energy flux, supported by holographic and free-field calculations.

Contribution

It proves a universal quadratic correction to charged entanglement entropy in general dimensions, linking it to fundamental theory coefficients and previous universal identities.

Findings

Quadratic correction is positive definite and universal.

Correction is controlled by coefficients $C_J$ and $a_2$.

Results are supported by holographic and free-field calculations.

Abstract

R\'enyi entropies, $S_n$, admit a natural generalization in the presence of global symmetries. These "charged R\'enyi entropies" are functions of the chemical potential $\mu$ conjugate to the charge contained in the entangling region and reduce to the usual notions as $\mu\rightarrow 0$. For $n=1$, this provides a notion of charged entanglement entropy. In this letter we prove that for a general $d (\geq 3)$-dimensional CFT, the leading correction to the uncharged entanglement entropy across a spherical entangling surface is quadratic in the chemical potential, positive definite, and universally controlled (up to fixed $d$-dependent constants) by the coefficients $C_J$ and $a_2$. These fully characterize, for a given theory, the current correlators $\langle JJ\rangle $ and $\langle TJJ \rangle$, as well as the energy flux measured at infinity produced by the insertion of the current operator. Our result is motivated by analytic holographic calculations for a special class of higher-curvature gravities coupled to a $(d-2)$-form in general dimensions as well as for free-fields in $d=4$. A proof for general theories and dimensions follows from previously known universal identities involving the magnetic response of twist operators introduced in arXiv:1310.4180 and basic thermodynamic relations.