Local subsystems in gauge theory and gravity
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 gaugeinvariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In YangMills 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 codimension2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension2 boundary, and positiondependent 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. Finally, our work suggests that the BekensteinHawking entropy may arise from the different ways of gluing together two partial Cauchy surfaces at a crosssection of themore »
 Authors:

^{[1]};
^{[2]}
 Univ. of California, Santa Barbara, CA (United States)
 Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)
 Publication Date:
 Grant/Contract Number:
 SC0011702
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 9; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Univ. of California, Santa Barbara, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; classical theories of gravity; spacetime symmetries; gauge symmetry
 OSTI Identifier:
 1360123
Donnelly, William, and Freidel, Laurent. Local subsystems in gauge theory and gravity. United States: N. p.,
Web. doi:10.1007/JHEP09(2016)102.
Donnelly, William, & Freidel, Laurent. Local subsystems in gauge theory and gravity. United States. doi:10.1007/JHEP09(2016)102.
Donnelly, William, and Freidel, Laurent. 2016.
"Local subsystems in gauge theory and gravity". United States.
doi:10.1007/JHEP09(2016)102. https://www.osti.gov/servlets/purl/1360123.
@article{osti_1360123,
title = {Local subsystems in gauge theory and gravity},
author = {Donnelly, William and Freidel, Laurent},
abstractNote = {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 gaugeinvariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In YangMills 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 codimension2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension2 boundary, and positiondependent 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. Finally, our work suggests that the BekensteinHawking entropy may arise from the different ways of gluing together two partial Cauchy surfaces at a crosssection of the horizon.},
doi = {10.1007/JHEP09(2016)102},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2016,
place = {United States},
year = {2016},
month = {9}
}