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

• Published in: Classical and quantum gravity Vol. 36; no. 19; pp. 195014 - 195054
• Main Authors: Freidel, Laurent, Livine, Etera, Pranzetti, Daniele
• Format: Journal Article
• Language: English
• Published: IOP Publishing 10.10.2019
• Subjects: edge modes; General Relativity and Quantum Cosmology; High Energy Physics - Theory; loop quantum gravity; Physics; quantum geometry; spacetime symmetry; Kac-Moody; string; general relativity; interface; Poincare; diffeomorphism; Bianchi identity; charge: surface; tube; Virasoro; conservation law; quantum gravity: loop space; Gauss law; spin: network
• ISSN: 0264-9381; 1361-6382
• DOI: 10.1088/1361-6382/ab40fe

We revisit the canonical framework for general relativity in its connection-vierbein formulation, recasting the Gauss law, the Bianchi identity and the space diffeomorphism bulk constraints as conservation laws for boundary surface charges, respectively electric, magnetic and momentum charges. Partitioning the space manifold into 3D regions glued together through their interfaces, we focus on a single domain and its punctured 2D boundary. The punctures carry a ladder of Kac-Moody edge modes, whose 0-modes represent the electric and momentum charges while the higher modes describe the stringy vibration modes of the 1D-boundary around each puncture. In particular, this allows to identify missing observables in the discretization scheme used in loop quantum gravity (LQG) and leads to an enhanced theory upgrading spin networks to tube networks carrying Virasoro representations. In the limit where the tubes are contracted to 1D links and the string modes neglected, we do not just recover LQG but obtain a more general structure: Poincaré charge networks, which carry a representation of the 3D diffeomorphism boundary charges on top of the fluxes and gauge transformations.