Origin of the quantum group symmetry in 3d quantum gravity
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866909876662304768 |
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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 |