3D $\mathcal{N}=1$ supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator
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| Format: | Preprint |
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2024
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| _version_ | 1866916599514005504 |
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| author | Bhattacharyya, Arpan Ghosh, Saptaswa Nandi, Poulami Pal, Sounak |
| author_facet | Bhattacharyya, Arpan Ghosh, Saptaswa Nandi, Poulami Pal, Sounak |
| contents | In this paper, we compute the partition functions of $\mathcal{N}=1$ SUGRA for different boundary topologies, i.e. sphere and torus, using super-Virasoro TQFT. We use fusion and modular kernels of the super-Liouville theory to compute the necklace-channel conformal block and showcase formalism by proving that the inner product holds for superconformal blocks, defined as states in the Hilbert space. Finally, we compute the out-of-time-order correlator for the torus topology with superconformal primary insertions as matter using the tools of super-Virasoro TQFT and investigate its early-time behaviour. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_01538 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 3D $\mathcal{N}=1$ supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator Bhattacharyya, Arpan Ghosh, Saptaswa Nandi, Poulami Pal, Sounak High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Quantum Physics In this paper, we compute the partition functions of $\mathcal{N}=1$ SUGRA for different boundary topologies, i.e. sphere and torus, using super-Virasoro TQFT. We use fusion and modular kernels of the super-Liouville theory to compute the necklace-channel conformal block and showcase formalism by proving that the inner product holds for superconformal blocks, defined as states in the Hilbert space. Finally, we compute the out-of-time-order correlator for the torus topology with superconformal primary insertions as matter using the tools of super-Virasoro TQFT and investigate its early-time behaviour. |
| title | 3D $\mathcal{N}=1$ supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2408.01538 |