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<p>In this paper, we compute the partition functions of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25468_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 1 SUGRA for different boundary topologies, i.e. punctured 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.</p>

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3D \( \mathcal{N} \) = 1 supergravity from Virasoro TQFT: gravitational partition function and Out-of-time-order correlator

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月6日

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  • Arpan Bhattacharyya,
  • Saptaswa Ghosh,
  • Poulami Nandi,
  • Sounak Pal

摘要

In this paper, we compute the partition functions of N \( \mathcal{N} \) = 1 SUGRA for different boundary topologies, i.e. punctured 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.