Matrix quantization of gravitational edge modes

          @misc{ pirsa_PIRSA:22100016,
            doi = {10.48660/22100016},
            url = {https://pirsa.org/22100016},
            author = {Speranza, Antony},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Matrix quantization of gravitational edge modes},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {oct},
            note = {PIRSA:22100016 see, \url{https://pirsa.org}}
          }
          

Abstract

The phase space of gravity restricted to a subregion bounded by a codimension-2 corner possesses an infinite-dimensional symmetry algebra consisting of diffeomorphisms of the 2-sphere and local SL(2,R) transformations of the normal planes. I will describe a deformation of a subalgebra preserving an area form on the sphere, and show that it leads to the finite dimensional algebra SU(N,N), reminiscent of older results concerning the fuzzy sphere, in which area-preserving diffeomorphisms are deformed to SU(N). This deformation is conjectured to be relevant to the quantization of the local gravitational phase space, and I will further demonstrate that the representation of SU(N,N) appearing in the quantization can be determined by matching the Casimir operators of the deformed algebra to classical phase space invariants. Based on 2012.10367 and upcoming work with W. Donnelly, L. Freidel, and S.F. Moosavian.