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Article
Report number	arXiv:2203.04325 ; IFT-UAM/CSIC-22-18 ; CERN-TH-2022-033
Title	Universal Feature of Charged Entanglement Entropy
Related title	A universal feature of charged entanglement entropy
Author(s)	Bueno, Pablo (CERN) ; Cano, Pablo A. (Leuven U.) ; Murcia, Ángel (Madrid, IFT) ; Rivadulla Sánchez, Alberto (Santiago de Compostela U.)
Publication	2022-07-06
Imprint	2022-03-08
Number of pages	13
In:	Phys. Rev. Lett. 129 (2022) 021601
DOI	10.1103/PhysRevLett.129.021601 (publication)
Subject category	gr-qc ; General Relativity and Cosmology ; hep-th ; Particle Physics - Theory
Abstract	Rényi entropies, $S_n$, admit a natural generalization in the presence of global symmetries. These "charged Rényi 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.
Copyright/License	publication: © 2022-2024 authors (License: CC BY 4.0), sponsored by SCOAP³ preprint: (License: arXiv nonexclusive-distrib 1.0)

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