Mathematical Physics and String Theory
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(23.01.) Gravitational edge modes: A new description of quantum geometry

Daniele Pranzetti (Perimeter)

23.01.2020 at 16:15

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 perfect setting to study the coarse-graining of gravity both
at the classical and the quantum levels

Arnold Sommerfeld Center
Theresienstrasse 37
Room 348