Three-dimensional $\operatorname{SL}(2,\mathbb R)$ Yang-Mills theory is three-dimensional gravity with background sources
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| Format: | Preprint |
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2024
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| _version_ | 1866917883803598848 |
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| author | Borsten, Leron Kanakaris, Dimitri Kim, Hyungrok |
| author_facet | Borsten, Leron Kanakaris, Dimitri Kim, Hyungrok |
| contents | Chern-Simons theory with certain gauge groups is known to be equivalent to a first-order formulation of three-dimensional Einstein gravity with a cosmological constant, where both are purely topological. Here, we extend this correspondence to theories with dynamical degrees of freedom. We show that three-dimensional Yang-Mills theory with gauge group $\operatorname{SL}(2,\mathbb R)$ is equivalent to the first-order formulation of three-dimensional Einstein gravity with no cosmological constant coupled to a background stress-energy tensor density (which breaks the diffeomorphism symmetry). The local degree of freedom of three-dimensional Yang-Mills theory corresponds to degenerate "gravitational waves" in which the metric is degenerate and the spin connection is no longer completely determined by the metric. Turning on a cosmological constant produces the third-way (for $Λ<0$) or the imaginary third-way (for $Λ>0$) gauge theories with a background stress-energy tensor density. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_14228 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Three-dimensional $\operatorname{SL}(2,\mathbb R)$ Yang-Mills theory is three-dimensional gravity with background sources Borsten, Leron Kanakaris, Dimitri Kim, Hyungrok High Energy Physics - Theory General Relativity and Quantum Cosmology 83C80 (Primary) 81T13, 81T20, 81T35, 83C55 (Secondary) Chern-Simons theory with certain gauge groups is known to be equivalent to a first-order formulation of three-dimensional Einstein gravity with a cosmological constant, where both are purely topological. Here, we extend this correspondence to theories with dynamical degrees of freedom. We show that three-dimensional Yang-Mills theory with gauge group $\operatorname{SL}(2,\mathbb R)$ is equivalent to the first-order formulation of three-dimensional Einstein gravity with no cosmological constant coupled to a background stress-energy tensor density (which breaks the diffeomorphism symmetry). The local degree of freedom of three-dimensional Yang-Mills theory corresponds to degenerate "gravitational waves" in which the metric is degenerate and the spin connection is no longer completely determined by the metric. Turning on a cosmological constant produces the third-way (for $Λ<0$) or the imaginary third-way (for $Λ>0$) gauge theories with a background stress-energy tensor density. |
| title | Three-dimensional $\operatorname{SL}(2,\mathbb R)$ Yang-Mills theory is three-dimensional gravity with background sources |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology 83C80 (Primary) 81T13, 81T20, 81T35, 83C55 (Secondary) |
| url | https://arxiv.org/abs/2408.14228 |