Two-form supergravity, superstring couplings, and Goldstino superfields in three dimensions

TL;DR

This paper develops off-shell supergravity formulations in three dimensions with gauge two-forms, enabling consistent superstring couplings and exploring models of spontaneously broken supersymmetry with Goldstino superfields.

Contribution

It introduces new off-shell supergravity models with gauge two-forms and demonstrates their use in superstring couplings and supersymmetry breaking.

Findings

Constructed off-shell ${ m AdS}$ supergravity with gauge two-forms.

Achieved superstring couplings that are $ppa$-symmetric and super-Weyl invariant.

Analyzed models of spontaneous supersymmetry breaking using Goldstino superfields.

Abstract

We develop off-shell formulations for ${\cal N}=1$ and ${\cal N}=2$ anti-de Sitter supergravity theories in three spacetime dimensions that contain gauge two-forms in the auxiliary field sector. These formulations are shown to allow consistent couplings of supergravity to the Green-Schwarz superstring with ${\cal N}=1$ or ${\cal N}=2$ spacetime supersymmetry. In addition to being $\kappa$-symmetric, the Green-Schwarz superstring actions constructed are also invariant under super-Weyl transformations of the target space. We also present a detailed study of models for spontaneously broken local supersymmetry in three dimensions obtained by coupling the known off-shell ${\cal N}=1$ and ${\cal N}=2$ supergravity theories to nilpotent Goldstino superfields.