Chern-Simons supergravities, with a twist

TL;DR

This paper explores noncommutative extensions of Chern-Simons supergravities in odd dimensions, focusing on a detailed example in five dimensions with specific gauge symmetry constraints.

Contribution

It introduces the first noncommutative version of D=5 CS supergravity, showing it exists only for the case N=4, thus identifying a unique consistent extension.

Findings

Noncommutative D=5 CS supergravity exists only for N=4

Explicit construction of the noncommutative supergravity model

Identification of gauge symmetry constraints for noncommutative extensions

Abstract

We discuss noncommutative extensions of Chern-Simons (CS) supergravities in odd dimensions. The example of D=5 CS supergravity, invariant under the gauge supergroup SU(2,2|N), is worked out in detail. Its noncommutative version is found to exist only for N=4.