论文标题
对称分辨的纠缠在广告$ {} _ 3 $/cft $ {} _ 2 $耦合到$ u（1）$ CHERN-SIMONS理论
Symmetry-Resolved Entanglement in AdS${}_3$/CFT${}_2$ coupled to $U(1)$ Chern-Simons Theory
论文作者
论文摘要
我们考虑在AD $ {} _ 3 $/cft $ {} _ 2 $耦合到$ u（1）$ Chern-Simons理论中的对称分解的纠缠熵。我们将二维形成式田间理论中充电矩的全息偶列为大部分Ads $ {} _ 3 $的带电威尔逊线，即ryu-takayanagi Geodesic Minimimilly在$ u（1）$ u（1）$ u（1）$ Chern-simons-simons仪表上。我们将Wilson系列周围的人类识别为Aharonov-Bohm阶段，在二维场理论中，该阶段是由收费的$ u（1）$ u（1）$ vertex运算符生成的，这些操作员插入了纠缠间隔的端点。此外，我们通过将带电矩的生成函数与纠缠子区域中的电荷量相关联，设计了一种新方法来计算对称性解决的纠缠熵。我们计算了由批量威尔逊线来源的$ U（1）$ Chern-Simons量规场的子区域费用。我们使用我们的方法来得出庞加莱补丁和全局广告$ {} _ 3 $的对称分解的纠缠熵以及锥形缺陷几何形状。在所有三种情况下，对称性解决的纠缠熵均由ryu-takayanagi Geodesic的长度和Chern-Simons级别$ k $确定，并实现了纠缠的电气。批量理论的渐近对称代数为$ \ hat {\ mathfrak {u}}} {（1）_K} $ kac-moody type。采用$ \ hat {\ mathfrak {u}} {（1）_k} $ kac-moody对称性，我们通过双重共形场理论中的计算确认了我们的全息结果。
We consider symmetry-resolved entanglement entropy in AdS${}_3$/CFT${}_2$ coupled to $U(1)$ Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS${}_3$, namely the Ryu-Takayanagi geodesic minimally coupled to the $U(1)$ Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged $U(1)$ vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the $U(1)$ Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS${}_3$, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level $k$, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $\hat{\mathfrak{u}}{(1)_k}$ Kac-Moody type. Employing the $\hat{\mathfrak{u}}{(1)_k}$ Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.
