Abstract
N=2 three dimensional Supergravity with internal $R-$symmetry generators can be understood as a two dimensional chiral Wess-Zumino-Witten model. In this paper, we present the reduced phase space description of the theory, which turns out to be flat limit of a generalised Liouville theory, up to zero modes. The reduced phase space description can also be explained as a gauged chiral Wess-Zumino-Witten model. We show that both these descriptions possess identical gauge and global (quantum N=2 superBMS$_3$) symmetries.
Highlights
AND SUMMARYThere is a connection between D þ 1-dimensional diffeomorphism invariant theories and D-dimensional field theories
One of the simplest contexts where this has been studied is 2 þ 1-dimensional gravity theories. It is a well-known fact that three-dimensional gravity can be described by a twodimensional field theory. 3D gravity solutions with nontrivial topology correspond to stress-energy tensors of a dual two-dimensional theory
The reduced dual theory in this case is, in general, a Wess-Zumino-Witten (WZW) model[3], defined on a closed spatial section, and is obtained by solving part of the constraints in the Chern-Simons theory[4,5,6]. Such reductions have been mostly performed for asymptotically anti–de Sitter 3D gravity [7,8,9,10,11,12,13,14,15], where the dual 2D theory is a conformal field theory with infinite-dimensional symmetry
Summary
There is a connection between D þ 1-dimensional diffeomorphism invariant theories and D-dimensional field theories. The dual chiral WZW model, when is gauged, shows invariance under infinite-dimensional quantum BMS3 algebra, which is the asymptotic symmetry of flat 3D gravity. The reduced phase space turns out to be a flat limit of a generalized super-Liouville-type theory and is identical to the dual chiral WZW model constructed in Ref. We shall write down the dual WZW model that describes the dynamics of the above theory (2.4) For this purpose, notice that the asymptotic gauge field (2.8) is highly constrained. Ð3:6Þ is a function of u and other fields do not transform
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