Origin of the quantum group symmetry in 3d quantum gravity

Fuente: arXiv
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Autores principales: Dupuis, Maïté, Freidel, Laurent, Girelli, Florian, Osumanu, Abdulmajid, Rennert, Julian
Formato: Preprint
Publicado: 2020
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author Dupuis, Maïté
Freidel, Laurent
Girelli, Florian
Osumanu, Abdulmajid
Rennert, Julian
author_facet Dupuis, Maïté
Freidel, Laurent
Girelli, Florian
Osumanu, Abdulmajid
Rennert, Julian
contents It is well-known that quantum groups are relevant to describe the quantum regime of 3d gravity. They encode a deformation of the gauge symmetries parametrized by the value of the cosmological constant. They appear as a form of regularization either through the quantization of the Chern-Simons formulation or the state sum approach of Turaev-Viro. Such deformations are perplexing from a continuum and classical picture since the action is defined in terms of undeformed gauge invariance. We present here a novel way to derive from first principle and from the classical action such quantum group deformation. The argument relies on two main steps. First we perform a canonical transformation, which deformed the gauge invariance and the boundary symmetries, and makes them depend on the cosmological constant. Second we implement a discretization procedure relying on a truncation of the degrees of freedom from the continuum.
format Preprint
id arxiv_https___arxiv_org_abs_2006_10105
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Origin of the quantum group symmetry in 3d quantum gravity
Dupuis, Maïté
Freidel, Laurent
Girelli, Florian
Osumanu, Abdulmajid
Rennert, Julian
General Relativity and Quantum Cosmology
High Energy Physics - Theory
Mathematical Physics
It is well-known that quantum groups are relevant to describe the quantum regime of 3d gravity. They encode a deformation of the gauge symmetries parametrized by the value of the cosmological constant. They appear as a form of regularization either through the quantization of the Chern-Simons formulation or the state sum approach of Turaev-Viro. Such deformations are perplexing from a continuum and classical picture since the action is defined in terms of undeformed gauge invariance. We present here a novel way to derive from first principle and from the classical action such quantum group deformation. The argument relies on two main steps. First we perform a canonical transformation, which deformed the gauge invariance and the boundary symmetries, and makes them depend on the cosmological constant. Second we implement a discretization procedure relying on a truncation of the degrees of freedom from the continuum.
title Origin of the quantum group symmetry in 3d quantum gravity
topic General Relativity and Quantum Cosmology
High Energy Physics - Theory
Mathematical Physics
url https://arxiv.org/abs/2006.10105