Dual versions of extended supergravities

TL;DR

This paper extends the concept of dual Lagrangian families in supergravity theories to N=3 and N=4 cases, revealing new models with spontaneous supersymmetry breaking and fixed scalar geometries.

Contribution

It constructs dual Lagrangian families for N=3 and N=4 supergravities with specific scalar geometries, expanding previous N=2 results and identifying models with spontaneous supersymmetry breaking.

Findings

Families of dual Lagrangians for N=3 and N=4 supergravities constructed.

Models with spontaneous supersymmetry breaking without cosmological term identified.

Scalar field geometries fixed, yet multiple dual formulations exist.

Abstract

Recently, using the model of N=2 supergravity -- vector multiplets interaction with the scalar field geometry $SU(1,m)/SU(m)\otimes U(1)$ as an example, we have shown that even when the scalar field geometry is fixed, one can have a whole family of the Lagrangians, which differ by vector field duality transformation. In this paper we carry out the construction of such families for the case of N=3 and N=4 supergravities, the scalar field geometry being $SU(3,m)/SU(3)\otimes SU(m)\otimes U(1)$ and $SU(1,1)/U(1)\otimes O(6,m)/O(6)\otimes O(m)$, correspondingly. Moreover, it turns out that these families contain, as a partial case, the models describing the interaction of arbitrary number of vector multiplets with our hidden sectors, admitting spontaneous supersymmetry breaking without a cosmological term.