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arXiv · 2006.10105

Origin of the quantum group symmetry in 3d quantum gravity

Maïté Dupuis·Laurent Freidel·Florian Girelli·Abdulmajid Osumanu·Julian Rennert
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Abstract

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.

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Maïté Dupuis, Laurent Freidel, Florian Girelli, Abdulmajid Osumanu, Julian Rennert. 2020-06-17. Origin of the quantum group symmetry in 3d quantum gravity. https://doi.org/10.1103/fr9h-3w7t

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