Twisted N=1, d=4 supergravity and its symmetries

TL;DR

This paper constructs a twisted superalgebra for N=1 Euclidean supergravity in four dimensions, revealing new symmetries and covariant structures on manifolds with an almost complex structure.

Contribution

It introduces a novel twisted superalgebra acting on supergravity fields, compatible with SU(2) symmetry, and details its couplings to matter multiplets.

Findings

Superalgebra contains 4 twisted supersymmetry generators.

Algebra closes on the twisted supergravity fields.

Couplings to matter multiplets are explicitly derived.

Abstract

We display the construction of a twisted superalgebra for the N=1 Euclidian supergravity on 4-manifolds with an almost complex structure. It acts on a representation of twisted supersymmetry made of forms with odd and even statistics and it is covariant under a SU(2)\subset SO(4) Lorentz invariance of the manifold's tangent-space. It contains 4 twisted supersymmetry generators, one nilpotent scalar, one vector and one pseudo-scalar. The superalgebra closes on the twisted fields of supergravity in its new minimal set of auxiliary fields. Its couplings to the twisted Wess and Zumino and vector multiplets are also determined.