期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 2, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP02(2018)021
关键词
Classical Theories of Gravity; Models of Quantum Gravity
资金
- National Science Foundation [PHY-1407744]
- Division Of Physics
- Direct For Mathematical & Physical Scien [1407744] Funding Source: National Science Foundation
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.
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