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002803444 005__ 20231004093405.0
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002803444 0247_ $$2DOI$$9APS$$a10.1103/PhysRevLett.129.021601$$qpublication
002803444 037__ $$9arXiv$$aarXiv:2203.04325$$chep-th
002803444 037__ $$aIFT-UAM/CSIC-22-18
002803444 037__ $$aCERN-TH-2022-033
002803444 035__ $$9arXiv$$aoai:arXiv.org:2203.04325
002803444 035__ $$9Inspire$$aoai:inspirehep.net:2048990$$d2023-10-03T09:08:35Z$$h2023-10-04T02:21:32Z$$mmarcxml$$ttrue$$uhttps://inspirehep.net/api/oai2d
002803444 035__ $$9Inspire$$a2048990
002803444 041__ $$aeng
002803444 100__ $$aBueno, Pablo$$uCERN$$vCERN, Theoretical Physics Department, CH-1211 Geneva 23, Switzerland
002803444 245__ $$9APS$$aUniversal Feature of Charged Entanglement Entropy
002803444 246__ $$9arXiv$$aA universal feature of charged entanglement entropy
002803444 269__ $$c2022-03-08
002803444 260__ $$c2022-07-06
002803444 300__ $$a13 p
002803444 520__ $$9APS$$aRényi entropies, <math display="inline"><msub><mi>S</mi><mi>n</mi></msub></math>, admit a natural generalization in the presence of global symmetries. These “charged Rényi entropies” are functions of the chemical potential <math display="inline"><mi>μ</mi></math> conjugate to the charge contained in the entangling region and reduce to the usual notions as <math display="inline"><mrow><mi>μ</mi><mo stretchy="false">→</mo><mn>0</mn></mrow></math>. For <math display="inline"><mi>n</mi><mo>=</mo><mn>1</mn></math>, this provides a notion of charged entanglement entropy. In this Letter, we prove that for a general <math display="inline"><mi>d</mi><mo stretchy="false">(</mo><mo>≥</mo><mn>3</mn><mo stretchy="false">)</mo></math>-dimensional conformal field theory, 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 <math display="inline"><mi>d</mi></math>-dependent constants) by the coefficients <math display="inline"><msub><mi>C</mi><mi>J</mi></msub></math> and <math display="inline"><msub><mi>a</mi><mn>2</mn></msub></math>. These fully characterize, for a given theory, the current correlators <math display="inline"><mrow><mo stretchy="false">⟨</mo><mrow><mi>J</mi><mi>J</mi></mrow><mo stretchy="false">⟩</mo></mrow></math> and <math display="inline"><mrow><mo stretchy="false">⟨</mo><mrow><mi>T</mi><mi>J</mi><mi>J</mi></mrow><mo stretchy="false">⟩</mo></mrow></math>, 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 (<math display="inline"><mrow><mi>d</mi><mo>-</mo><mn>2</mn></mrow></math>) form in general dimensions as well as for free fields in <math display="inline"><mi>d</mi><mo>=</mo><mn>4</mn></math>. A proof for general theories and dimensions follows from previously known universal identities involving the magnetic response of twist operators introduced in A. Belin et al. [J. High Energy Phys. 12 (2013) 059.] and basic thermodynamic relations.
002803444 520__ $$9arXiv$$aRényi entropies, $S_n$, admit a natural generalization in the presence of global symmetries. These "charged Rényi entropies" are functions of the chemical potential $\mu$ conjugate to the charge contained in the entangling region and reduce to the usual notions as $\mu\rightarrow 0$. For $n=1$, this provides a notion of charged entanglement entropy. In this letter we prove that for a general $d (\geq 3)$-dimensional CFT, the leading correction to the uncharged entanglement entropy across a spherical entangling surface is quadratic in the chemical potential, positive definite, and universally controlled (up to fixed $d$-dependent constants) by the coefficients $C_J$ and $a_2$. These fully characterize, for a given theory, the current correlators $\langle JJ\rangle $ and $\langle TJJ \rangle$, as well as the energy flux measured at infinity produced by the insertion of the current operator. Our result is motivated by analytic holographic calculations for a special class of higher-curvature gravities coupled to a $(d-2)$-form in general dimensions as well as for free-fields in $d=4$. A proof for general theories and dimensions follows from previously known universal identities involving the magnetic response of twist operators introduced in arXiv:1310.4180 and basic thermodynamic relations.
002803444 540__ $$3preprint$$aarXiv nonexclusive-distrib 1.0$$uhttp://arxiv.org/licenses/nonexclusive-distrib/1.0/
002803444 540__ $$3publication$$aCC BY 4.0$$fSCOAP3$$uhttps://creativecommons.org/licenses/by/4.0/
002803444 542__ $$3publication$$dauthors$$g2022
002803444 65017 $$2arXiv$$agr-qc
002803444 65017 $$2SzGeCERN$$aGeneral Relativity and Cosmology
002803444 65017 $$2arXiv$$ahep-th
002803444 65017 $$2SzGeCERN$$aParticle Physics - Theory
002803444 690C_ $$aCERN
002803444 690C_ $$aARTICLE
002803444 700__ $$aCano, Pablo A.$$uLeuven U.$$vInstituut voor Theoretische Fysica, KU Leuven. Celestijnenlaan 200D, B-3001 Leuven, Belgium
002803444 700__ $$aMurcia, Ángel$$uMadrid, IFT$$vInstituto de Física Teórica UAM/CSIC, C/ Nicolás Cabrera, 13-15, C.U. Cantoblanco, 28049 Madrid, Spain
002803444 700__ $$aRivadulla Sánchez, Alberto$$uSantiago de Compostela U.$$vInstituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain$$vDepartamento de Física de Partículas, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain
002803444 773__ $$c021601$$mpublication$$n2$$pPhys. Rev. Lett.$$v129$$y2022
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