Dimensional reduction of the S 3/WZW duality

Kenta Suzuki (Department of Physics, Rikkyo University, Toshima, Tokyo, 171-8501, Japan) ; Yusuke Taki (Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan)

Recently proposed duality relates the critical level limit $$\widehat{k}\to -2$$ of $${\text{SU}}{\left(2\right)}_{\widehat{k}}$$ WZW models to a classical three-dimensional Einstein gravity on a sphere. In this paper, we propose a dimensional reduced version of this duality. The gravity side is reduced to a Jackiw-Teitelboim (JT) gravity on S 2 with a non-standard boundary term, or a BF theory with SU(2) gauge symmetry. At least in low temperature limit, these two-dimensional gravity theories completely capture the original three-dimensional gravity effect. The CFT side is reduced to a certain complex Liouville quantum mechanics (LQM) with SU(2) gauge symmetry. Our proposal gives an interesting example of a holography without boundary. We also discuss a higher-spin generalization with SU(N) gauge symmetry.

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      "source": "Springer", 
      "value": "Recently proposed duality relates the critical level limit  $$\\widehat{k}\\to -2$$  of  $${\\text{SU}}{\\left(2\\right)}_{\\widehat{k}}$$  WZW models to a classical three-dimensional Einstein gravity on a sphere. In this paper, we propose a dimensional reduced version of this duality. The gravity side is reduced to a Jackiw-Teitelboim (JT) gravity on S 2 with a non-standard boundary term, or a BF theory with SU(2) gauge symmetry. At least in low temperature limit, these two-dimensional gravity theories completely capture the original three-dimensional gravity effect. The CFT side is reduced to a certain complex Liouville quantum mechanics (LQM) with SU(2) gauge symmetry. Our proposal gives an interesting example of a holography without boundary. We also discuss a higher-spin generalization with SU(N) gauge symmetry."
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Published on:
15 March 2024
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2024 (2024)
Issue 3
Pages 1-33
DOI:
https://doi.org/10.1007/JHEP03(2024)103
arXiv:
2309.13852
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: