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arXiv · 2309.13852

Dimensional Reduction of the $S^3$/WZW Duality

Kenta Suzuki·Yusuke Taki
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Abstract

Recently proposed duality relates the critical level limit $\hat{k} \to -2$ of $SU(2)_{\hat{k}}$ 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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Kenta Suzuki, Yusuke Taki. 2023-09-25. Dimensional Reduction of the $S^3$/WZW Duality. https://arxiv.org/abs/2309.13852

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