Abstract
We discuss the symplectic diffeomorphisms of a class of supermanifolds and the structure of the underlying infinite dimensional superalgebras. We construct a Chern-Simons (CS) gauge theory in (2+1) dimensions for these algebras. There exists a finite dimensional supersymmetric truncation which is the (2 n − 1)-dimensional hamiltonian superalgebra H ̃ (n) . With a central charge added, it is a superalgebra, C(n) , associated with a Clifford algebra. We find an embedding of d=3, N=2 anti-de Sitter superalgebra OSp(2|2) ⊗ OSp (2|2) in C (4), and construct a CS action for its infinite dimensional extension. We also discuss the construction fdof a CS action for the infinite dimensional extension of the d=3, N=2 superconformal algebra OSp(2, 4).
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