论文标题
U（1）CS理论与SL（2）CS公式：边界理论和威尔逊线
U(1) CS Theory vs SL(2) CS Formulation: Boundary Theory and Wilson Line
论文作者
论文摘要
我们首先从U（1）Chern-Simons理论得出边界理论。 $ n $ -sheet歧管上的边界动作从威尔逊线的后反应出现。原因是U（1）Chern-Simons理论在引入威尔逊线时可以提供确切的有效动作。纯广告中的威尔逊线$ _3 $爱因斯坦重力等同于边界理论中的纠缠熵，直到经典重力。 U（1）Chern-Simons理论以自我相互作用项偏离边界上的规格。我们还将SL（2）Chern-Simons公式中的Hayward术语与Wilson Line方法进行了比较。引入两个楔子可以在经典级别重现单个间隔的纠缠熵。我们通过结合大量和海沃德项来提出量子泛化。分区函数的量子校正消失。最后，我们计算单个间隔的纠缠熵。纯广告$ _3 $爱因斯坦重力理论在单环级上显示了中央电荷的转移26。 U（1）Chern-Simons理论并未显示出与量子效应的转变。结果在弱重力常数极限中是相同的。非变化量子校正表明Hayward项不正确。
We first derive the boundary theory from the U(1) Chern-Simons theory. The boundary action on an $n$-sheet manifold appears from its back-reaction of the Wilson line. The reason is that the U(1) Chern-Simons theory can provide an exact effective action when introducing the Wilson line. The Wilson line in the pure AdS$_3$ Einstein gravity is equivalent to entanglement entropy in the boundary theory up to classical gravity. The U(1) Chern-Simons theory deviates by a self-interaction term from the gauge formulation on the boundary. We also compare the Hayward term in the SL(2) Chern-Simons formulation to the Wilson line approach. Introducing two wedges can reproduce the entanglement entropy for a single interval at the classical level. We propose quantum generalization by combining the bulk and Hayward terms. The quantum correction of the partition function vanishes. In the end, we calculate the entanglement entropy for a single interval. The pure AdS$_3$ Einstein gravity theory shows a shift of central charge by 26 at the one-loop level. The U(1) Chern-Simons theory does not show a shift from the quantum effect. The result is the same in the weak gravitational constant limit. The non-vanishing quantum correction shows that the Hayward term is incorrect.
