A BV action for 3D supergravity is obtained by proving the Rarita-Schwinger theory is symplectomorphic to a BF supergravity AKSZ theory.
Boundary structure of gauge and matter fields coupled to gravity
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abstract
The boundary structure of $3+1$-dimensional gravity (in the Palatini-Cartan formalism) coupled to to gauge (Yang-Mills) and matter (scalar and spinorial) fields is described through the use of the Kijowski-Tulczijew construction. In particular, the reduced phase space is obtained as the reduction of a symplectic space by some first class constraints and a cohomological description (BFV) of it is presented.
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3D Supergravity in the Batalin-Vilkovisky Formalism
A BV action for 3D supergravity is obtained by proving the Rarita-Schwinger theory is symplectomorphic to a BF supergravity AKSZ theory.