论文标题
拓扑字符串理论中的纠缠熵和边缘模式II：双仪理论故事
Entanglement entropy and edge modes in topological string theory II: The dual gauge theory story
论文作者
论文摘要
这是两部分的第二部分，该论文致力于研究模型拓扑弦理论中的纠缠熵和边缘模式。该理论具有量规（Gopakumar-VAFA）二元性，这是ADS/CFT的拓扑类似物。在第1部分中，我们定义了解决方案的拓扑封闭弦理论的广义熵概念。我们根据Hartle-Hawking状态的Q形成的纠缠熵提供了对广义熵的规范解释。我们发现在量子组对称性下转换的弦边模式并将其解释为纠缠麸皮。在这项工作中，我们提供了双重CHERN-SIMONS仪表理论描述。使用gopakumar-vafa二元性，我们将封闭的弦理论映射到chern-simons理论状态，其中包含威尔逊循环的叠加。这些Wilson循环是确定已解决的Conifold的分区函数的封闭弦的世界表偶。我们表明，由于切割这些Wilson循环而导致的未变形的纠缠熵再现了大量的广义熵，因此捕获了散装时空的纠缠。最后，我们表明，在gopakumar-vafa二元性下，批量的纠缠麸皮被映射到拓扑d-branes的构型，并且在块状的非本地纠缠边界条件映射到量规理论二元组中的局部边界条件。这表明量规弦双重性的基础几何过渡也可能是纠缠麸皮的出现。
This is the second in a two-part paper devoted to studying entanglement entropy and edge modes in the A model topological string theory. This theory enjoys a gauge-string (Gopakumar-Vafa) duality which is a topological analogue of AdS/CFT. In part 1, we defined a notion of generalized entropy for the topological closed string theory on the resolved conifold. We provided a canonical interpretation of the generalized entropy in terms of the q-deformed entanglement entropy of the Hartle-Hawking state. We found string edge modes transforming under a quantum group symmetry and interpreted them as entanglement branes. In this work, we provide the dual Chern-Simons gauge theory description. Using Gopakumar-Vafa duality, we map the closed string theory Hartle-Hawking state to a Chern-Simons theory state containing a superposition of Wilson loops. These Wilson loops are dual to closed string worldsheets that determine the partition function of the resolved conifold. We show that the undeformed entanglement entropy due to cutting these Wilson loops reproduces the bulk generalized entropy and therefore captures the entanglement underlying the bulk spacetime. Finally, we show that under the Gopakumar-Vafa duality, the bulk entanglement branes are mapped to a configuration of topological D-branes, and the non-local entanglement boundary condition in the bulk is mapped to a local boundary condition in the gauge theory dual. This suggests that the geometric transition underlying the gauge-string duality may also be responsible for the emergence of entanglement branes.
