Local phase space and edge modes for diffeomorphism-invariant theories
Local phase space and edge modes for diffeomorphism-invariant theories
复制标题
微分同胚不变理论的局部相空间和边缘模式
DOI：
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发表时间：
2018
影响因子：
5.4
通讯作者：
A. Speranza
中科院分区：
文献类型：
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作者：
A. Speranza
讨论了用Donnelly和Freidel[36]的扩展相空间表征微分同态不变理论中子区域局部自由度的一种方法。这样的表征对于定义引力理论中的局部可观测值和纠缠熵是重要的。传统的子区域相空间构造对于作用于边界的微分同态是不不变的。扩展相空间通过在边界处引入边缘模场来解决这一问题，边缘模场在微分同态下的变换使扩展辛结构完全规范不变。在这项工作中，我们提出了边模辛结构的一般构造。我们证明了新场满足由与边缘模式场相关的诺特电荷产生的表面对称代数。对于保曲面对称，该代数对于所有的微分同态不变理论是通用的，包括边界的微分同态，法平面的SL（2, 1）变换，以及在某些情况下的法向剪切变换。我们还表明，如果边界条件的选择，使表面平移是对称的，代数获得一个中心扩展。
We discuss an approach to characterizing local degrees of freedom of a subregion in diffeomorphism-invariant theories using the extended phase space of Donnelly and Freidel [36]. Such a characterization is important for defining local observables and entanglement entropy in gravitational theories. Traditional phase space constructions for subregions are not invariant with respect to diffeomorphisms that act at the boundary. The extended phase space remedies this problem by introducing edge mode fields at the boundary whose transformations under diffeomorphisms render the extended symplectic structure fully gauge invariant. In this work, we present a general construction for the edge mode symplectic structure. We show that the new fields satisfy a surface symmetry algebra generated by the Noether charges associated with the edge mode fields. For surface-preserving symmetries, the algebra is universal for all diffeomorphism-invariant theories, comprised of diffeomorphisms of the boundary, SL(2, ℝ) transformations of the normal plane, and, in some cases, normal shearing transformations. We also show that if boundary conditions are chosen such that surface translations are symmetries, the algebra acquires a central extension.