OSp(1|4) supergravity and its noncommutative extension

TL;DR

This paper reviews OSp(1|4)-invariant N=1, D=4 supergravity and introduces a noncommutative extension using a star-product, resulting in a higher derivative supergravity theory that reduces to standard supergravity when the deformation parameter vanishes.

Contribution

It presents the first noncommutative extension of OSp(1|4) supergravity using a geometric Seiberg-Witten map, maintaining gauge invariance and reducing to classical supergravity in the commutative limit.

Findings

Constructed a noncommutative supergravity model with star-product deformation.

Demonstrated gauge invariance under OSp(1|4) and Lorentz transformations.

Showed the classical limit recovers standard N=1, D=4 AdS supergravity.

Abstract

We review the OSp(1|4)-invariant formulation of N=1, D=4 supergravity and present its noncommutative extension, based on a star-product originating from an abelian twist with deformation parameter \theta. After use of a geometric generalization of the Seiberg-Witten map, we obtain an extended (higher derivative) supergravity theory, invariant under usual OSp(1|4) gauge transformations. Gauge fixing breaks the OSp(1|4) symmetry to its Lorentz subgroup, and yields a Lorentz invariant extended theory whose classical limit \theta --> 0 is the usual N=1, D=4 AdS supergravity.