Dimensional reduction of the S 3/WZW duality

Abstract 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 si...

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Bibliographic Details
Published in:The journal of high energy physics 2024-03, Vol.2024 (3), p.1-33
Main Authors: Kenta Suzuki, Yusuke Taki
Format: Article
Language:English
Subjects:
2D Gravity
de Sitter space
Gauge-Gravity Correspondence
Online Access:Get full text
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Summary:Abstract 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.
ISSN:1029-8479
DOI:10.1007/JHEP03(2024)103