Five-dimensional gravitational super Chern-Simons terms

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Supergravity, Field Theories In Dimensions Other Than Four

Scientific paper

We consider the Chern-Simons five-form C5(CS) for the five-dimensional anti-de Sitter superalgebra SU(2,2||1), whose exterior derivative is equal to dABCRCRBRA where RA are the full group curvatures and dABC are the invariant d symbols of SU(2,2||1). Under the simple local five-dimensional supersymmetry transformations, C5(CS) is not invariant. Its relation to the invariant action of simple five-dimensional supergravity in the group-manifold formulation is given.

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