论文标题
充电纠缠熵的普遍特征
A universal feature of charged entanglement entropy
论文作者
论文摘要
rényi熵，$ s_n $，在全球对称性的存在下承认自然概括。这些“带电的rényi熵”是化学势$μ$偶联到纠缠区域中的电荷的功能，并将其减少为通常的概念，为$μ\ rightarrow 0 $。对于$ n = 1 $，这提供了充电纠缠熵的概念。在这封信中，我们证明，对于一般的$ d（\ geq 3）$ - 尺寸CFT，对跨球形纠缠表面无负荷的纠缠熵的领先纠正在化学势，正定和普遍控制的化学电位上是二次的（由固定的$ d $ d $ c_j $ c_j $ $ c_j $ a __________2 $ a__2 $ a__2 $ c_j $ a__2 $ c_j $ a_2。这些完全表征了当前的相关器$ \ langle jj \ rangle $和$ \ langle tjj \ rangle $，以及由当前操作员插入产生的无限元。我们的结果是由一类特殊类别的高素质重力的分析全息计算，结合了$（d-2）$的一般维度以及$ d = 4 $的自由场。一般理论和维度的证明遵循先前已知的通用认同，涉及ARXIV中引入的扭曲算子的磁反应：1310.4180和基本的热力学关系。
Rényi entropies, $S_n$, admit a natural generalization in the presence of global symmetries. These "charged Rényi entropies" are functions of the chemical potential $μ$ conjugate to the charge contained in the entangling region and reduce to the usual notions as $μ\rightarrow 0$. 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.
