Edge modes and corner ambiguities in 3d Chern-Simons theory and gravity
Edge modes and corner ambiguities in 3d Chern-Simons theory and gravity
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DOI：
10.1016/j.nuclphysb.2017.09.010
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发表时间：
2017-11-01
影响因子：
2.8
通讯作者：
Geiller, Marc
中科院分区：
文献类型：
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作者：
Geiller, Marc
规范场论中的边界是许多有趣现象的轨迹，例如全息原理或AdS/CFT和体边界对应。特别是，人们已经认识到边界可以打破规范不变性，从而将规范自由度转化为物理自由度。然而，没有已知的系统的方法来识别这些自由度和可能的相关边界观测。根据Donnelly和Freidel最近的工作，我们证明了这可以通过扩展协变哈密顿形式主义来实现，从而使其在任意大规范变换下具有规范不变。这可以通过引入新的边界场来扩展相空间，这反过来又确定了新的边界对称性和可观测量。我们提出了这个建设背后的一般框架，并找到它可以适用于任意拉格朗日的条件。通过研究阿贝尔Chern-Simons理论和一阶三维引力的例子，我们证明了新的边界观测量满足相应的Kac-Moody仿射代数.这表明，这个新的扩展相空间公式确实正确地描述了动力学边界自由度，并给予信贷的情况下，以前已经推导出的结果？我们期望这种对边界对称性的系统理解将在有限区域的引力量子化中发挥重要作用。(C)2017作者由爱思唯尔公司出版
Boundaries in gauge field theories are known to be the locus of a wealth of interesting phenomena, as illustrated for example by the holographic principle or by the AdS/CFT and bulk-boundary correspondences. In particular, it has been acknowledged for quite some time that boundaries can break gauge invariance, and thereby turn gauge degrees of freedom into physical ones. There is however no known systematic way of identifying these degrees of freedom and possible associated boundary observables. Following recent work by Donnelly and Freidel, we show that this can be achieved by extending the covariant Hamiltonian formalism so as to make it gauge-invariant under arbitrary large gauge transformations. This can be done at the expense of extending the phase space by introducing new boundary fields, which in turn determine new boundary symmetries and observables. We present the general framework behind this construction, and find the conditions under which it can be applied to an arbitrary Lagrangian. By studying the examples of Abelian Chern-Simons theory and first order three-dimensional gravity, we then show that the new boundary observables satisfy the known corresponding Kac-Moody affine algebras. This shows that this new extended phase space formulation does indeed properly describe the dynamical boundary degrees of freedom, and gives credit to the results which have been previously derived in the case of diffeomorphism symmetry. We expect that this systematic understanding of the boundary symmetries will play a major role for the quantization of gravity in finite regions. (C) 2017 The Author. Published by Elsevier B.V.