Symmetry TFTs for Continuous Spacetime Symmetries
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908535859707904 |
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| author | Apruzzi, Fabio Dondi, Nicola Etxebarria, Iñaki García Lam, Ho Tat Schafer-Nameki, Sakura |
| author_facet | Apruzzi, Fabio Dondi, Nicola Etxebarria, Iñaki García Lam, Ho Tat Schafer-Nameki, Sakura |
| contents | We propose a Symmetry Topological Field Theory (SymTFT) for continuous spacetime symmetries. For a $d$-dimensional theory, it is given by a $(d+1)$-dimensional BF-theory for the spacetime symmetry group, and whenever $d$ is even, it can also include Chern-Simons couplings that encode conformal and gravitational anomalies. We study the boundary conditions for this SymTFT and describe the general setup to study symmetry breaking of spacetime symmetries. We then specialize to the conformal symmetry case and derive the dilaton action for conformal symmetry breaking. To further substantiate that our setup captures spacetime symmetries, we demonstrate that the topological defects of the SymTFT realize the associated spacetime symmetry transformations. Finally, we study the relation to gravity and holography. The proposal classically coincides with two-dimensional Jackiw-Teitelboim gravity for $d=1$ as well as the topological limit of four-dimensional gravity in the $d=3$ case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetry TFTs for Continuous Spacetime Symmetries Apruzzi, Fabio Dondi, Nicola Etxebarria, Iñaki García Lam, Ho Tat Schafer-Nameki, Sakura High Energy Physics - Theory Strongly Correlated Electrons General Relativity and Quantum Cosmology We propose a Symmetry Topological Field Theory (SymTFT) for continuous spacetime symmetries. For a $d$-dimensional theory, it is given by a $(d+1)$-dimensional BF-theory for the spacetime symmetry group, and whenever $d$ is even, it can also include Chern-Simons couplings that encode conformal and gravitational anomalies. We study the boundary conditions for this SymTFT and describe the general setup to study symmetry breaking of spacetime symmetries. We then specialize to the conformal symmetry case and derive the dilaton action for conformal symmetry breaking. To further substantiate that our setup captures spacetime symmetries, we demonstrate that the topological defects of the SymTFT realize the associated spacetime symmetry transformations. Finally, we study the relation to gravity and holography. The proposal classically coincides with two-dimensional Jackiw-Teitelboim gravity for $d=1$ as well as the topological limit of four-dimensional gravity in the $d=3$ case. |
| title | Symmetry TFTs for Continuous Spacetime Symmetries |
| topic | High Energy Physics - Theory Strongly Correlated Electrons General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2509.07965 |