Abstract
We consider minimal supergravity on (2+1)dimensional de-Sitter background. We fix the fall-off conditions for gravitini fields in order to fix the asymptotic phase space. Using the Chern-Simons formulation, we then derive the asymptotic symmetry algebra for this theory. The fall-off conditions impose constraints on the phase space which reduces the Chern Simons theory to a WZW model. Further constraints reduce it to a super-Liouville theory at the boundary. This can be treated as a classical dual for the supergravity theory in the bulk.
Highlights
The seminal work of Brown and Henneaux [1] provided us with the precursor of holographic duality in the case of ð2 þ 1ÞD gravity
Their work suggested that an asymptotic symmetry group of locally AdS3 backgrounds gives rise to centrally extended Virasoro algebra at the boundary, which is the symmetry algebra for 2D conformal field theories
A direct analytic extension of AdS=CFT ideas would suggest that the dual theory lives both in the past (I−) and future boundary (Iþ) of dS
Summary
The Einstein action can be written as a sum of CS actions of A and A , SEH 1⁄4 −iSκ1⁄2A þ iSκ1⁄2A ; ð2:4Þ where Sκ1⁄2A is the Chern-Simons action given by. Its equations of motion are just F 1⁄4 0, where F is the field strength given by F 1⁄4 dA þ A ∧ A This means that the field A is locally pure gauge, and the solution can be written in the form A 1⁄4 G−1dG, where G is an SLð2; CÞ element. In terms of the component fields, the equations of motion become dec þ εcabeaωb þ ðσcεÞαβðψ αψ β − χαχβÞ 1⁄4 0; dωc þ. This we present here just for completeness. For the λ → 0 limit, these equations get decoupled and a generic solution is possible [19]
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