Donnelly William, Jiang Yikun, Kim Manki, Wong Gabriel
Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, ON N2L 2Y5 Canada.
Department of Physics, Cornell University, Ithaca, New York USA.
J High Energy Phys. 2021;2021(10):201. doi: 10.1007/JHEP10(2021)201. Epub 2021 Oct 26.
Progress in identifying the bulk microstate interpretation of the Ryu-Takayanagi formula requires understanding how to define entanglement entropy in the bulk closed string theory. Unfortunately, entanglement and Hilbert space factorization remains poorly understood in string theory. As a toy model for AdS/CFT, we study the entanglement entropy of closed strings in the topological A-model in the context of Gopakumar-Vafa duality. We will present our results in two separate papers. In this work, we consider the bulk closed string theory on the resolved conifold and give a self-consistent factorization of the closed string Hilbert space using extended TQFT methods. We incorporate our factorization map into a Frobenius algebra describing the fusion and splitting of Calabi-Yau manifolds, and find string edge modes transforming under a -deformed surface symmetry group. We define a string theory analogue of the Hartle-Hawking state and give a canonical calculation of its entanglement entropy from the reduced density matrix. Our result matches with the geometrical replica trick calculation on the resolved conifold, as well as a dual Chern-Simons theory calculation which will appear in our next paper [1]. We find a realization of the Susskind-Uglum proposal identifying the entanglement entropy of closed strings with the thermal entropy of open strings ending on entanglement branes. We also comment on the BPS microstate counting of the entanglement entropy. Finally we relate the nonlocal aspects of our factorization map to analogous phenomenon recently found in JT gravity.
在确定Ryu-Takayanagi公式的整体微观态解释方面取得进展，需要理解如何在整体闭弦理论中定义纠缠熵。不幸的是，在弦理论中，纠缠和希尔伯特空间分解仍然理解得很差。作为AdS/CFT的一个玩具模型，我们在Gopakumar-Vafa对偶的背景下研究拓扑A模型中闭弦的纠缠熵。我们将在两篇独立的论文中展示我们的结果。在这项工作中，我们考虑在已解决的锥形流形上的整体闭弦理论，并使用扩展的TQFT方法对闭弦希尔伯特空间进行自洽分解。我们将我们的分解映射纳入一个描述卡拉比-丘流形融合和分裂的弗罗贝尼乌斯代数中，并发现弦边模式在一个变形的表面对称群下变换。我们定义了哈特尔-霍金态的弦理论类似物，并从约化密度矩阵对其纠缠熵进行了规范计算。我们的结果与在已解决的锥形流形上的几何复制技巧计算以及将出现在我们下一篇论文[1]中的对偶陈-西蒙斯理论计算相匹配。我们发现了苏斯金德-乌格鲁姆提议的一种实现，即将闭弦的纠缠熵与终止于纠缠膜上的开弦的热熵等同起来。我们还评论了纠缠熵的BPS微观态计数。最后，我们将我们分解映射的非局部方面与最近在JT引力中发现的类似现象联系起来。
