PIRSA:20040083

Gravitational edge modes: From Kac-Moody charges to Poincaré networks

Pranzetti, D. (2020). Gravitational edge modes: From Kac-Moody charges to Poincaré networks. Perimeter Institute. https://pirsa.org/20040083

Pranzetti, Daniele. Gravitational edge modes: From Kac-Moody charges to Poincaré networks. Perimeter Institute, Apr. 02, 2020, https://pirsa.org/20040083 

          @misc{ pirsa_PIRSA:20040083,
            doi = {10.48660/20040083},
            url = {https://pirsa.org/20040083},
            author = {Pranzetti, Daniele},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Gravitational edge modes: From Kac-Moody charges to Poincar{\'e} networks},
            publisher = {Perimeter Institute},
            year = {2020},
            month = {apr},
            note = {PIRSA:20040083 see, \url{https://pirsa.org}}
          }

Daniele Pranzetti University of Udine

DOI 10.48660/20040083
Collection
Talk Type Scientific Series
Subject

Abstract

In this talk I revisit the canonical framework for general relativity in its connection-frame field formulation, exploiting its local holographic nature. I will show how we can understand  the  Gauss law, the Bianchi identity and the space diffeomorphism constraints as conservation laws for local surface charges. These charges being respectively the electric flux, the dual magnetic flux  and momentum charges. Quantization of the surface charge algebra can be done in terms of Kac-Moody edge modes. This leads to an enhanced theory upgrading spin networks to tube networks carrying Virasoro representations. Taking a finite dimensional truncation of this quantization yields states of quantum geometry,  dubbed `Poincaré charge networks’, which carry a representation of the 3D diffeomorphism boundary charges on top of the SU(2) fluxes and gauge transformations. This opens the possibility to have for the first time a framework where spatial diffeomorphism are represented at the quantum level. Moreover, our construction leads naturally to the picture that the relevant geometrical degrees of freedom live on boundaries, that their dynamics and the fabric of quantum space itself is encoded into their entanglement, and it is designed to offer a new setting to study the coarse-graining of gravity both at the classical and the quantum levels.