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arXiv 1601.04744hep-thgr-qc
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规范理论和引力中的局域子系统

Local subsystems in gauge theory and gravity

William Donnelly, Laurent Freidel

摘要:

考虑了在规范理论和引力中定义定域子系统的问题。这样的系统与具有边界的类空超曲面相关联,并为研究空间区域的纠缠熵提供了自然的环境。通过在边界上引入新的自由度,我们给出了一种将规范不变的经典相空间与带边界的空间切片相关联的一般形式。在杨-米尔斯理论中,新的自由度是边界上规范的选择,其变换由非阿贝尔电场的法向分量产生。在广义相对论中,新的自由度是余维2曲面的位置和共形法坐标系的选择。这些自由度变换下的一组表面对称性,包括余维2边界的同构,和位置相关的线性变形的法平面。我们发现产生这些对称性的可观测量,包括共形正常度量和曲率的正常连接。我们讨论了在量子引力中定义纠缠熵的问题。我们的工作表明,贝肯斯坦-霍金熵可能产生于在视界横截面上将两个部分柯西曲面粘合在一起的不同方式。

英文摘要:

We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of regions of space. We present a general formalism to associate a gauge-invariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a choice of gauge on the boundary, transformations of which are generated by the normal component of the nonabelian electric field. In general relativity the new degrees of freedom are the location of a codimension-2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension-2 boundary, and position-dependent linear deformations of its normal plane. We find the observables which generate these symmetries, consisting of the conformal normal metric and curvature of the normal connection. We discuss the implications for the problem of defining entanglement entropy in quantum gravity. Our work suggests that the Bekenstein-Hawking entropy may arise from the different ways of gluing together two partial Cauchy surfaces at a cross-section of the horizon.

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