Dimensional reduction of the S3/WZW duality

A bstract Recently proposed duality relates the critical level limit k→ -2 of SU(2)_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.