Local subsystems in gauge theory and gravity
By William Donnelly, L. Freidel. 2016
417 citations recorded by the source corpus.
A bstractWe 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 localized subsystems. 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.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/8a1df0d608acde9a19b612f0c6a09df3226dea70
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Citations in the corpus
- Symmetries and charges of general relativity at null boundaries (2018, methodology): “The covariant phase space formalism for spacetimes with boundary is also important in studying the contribution of edge modes to entanglement entropy in gauge theories and gravity [34, 35].”
- Observables, gravitational dressing, and obstructions to locality and subsystems (2016, background): “Another alternative is to define operators using additional, auxiliary structure such as considered in [12].”
- Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space (2016, background): “These charges are analogous to the edge modes of the electromagnetic field discussed in [23, 24], or the “center” in [25], or horizon symmetries in [26] (see also [34]).”
- Edge modes of gravity. Part I. Corner potentials and charges (2020, methodology): “In particular, while both formulations have diff(S) as a part of the corner symmetries, the Einstein–Hilbert formulation has an extra sl(2,R) corner symmetry [51], called the boost symmetry and denoted sl(2,R)⊥, which is trivially represented in the canonical case.”