The 3-Form Multiplet in Supergravity

TL;DR

This work formulates the coupling of the 3-form supermultiplet to the full supergravity–matter–Yang-Mills system using $U_K(1)$ superspace. It derives the constrained structure, identifies the component fields, and provides invariant component actions, including a scalar potential where the 3-form shifts the effective superpotential by a term proportional to the auxiliary constant $c$. The results yield two key applications: a fundamental 3-form arising in strong–weak duality via dimensional reduction and a composite 3-form describing gaugino condensates with a VY–type superpotential. The framework clarifies how 3-forms interact with dilaton-like moduli and Yang-Mills sectors, with implications for cosmological constant handling and SUSY breaking in effective string-inspired theories.

Abstract

We derive the couplings of the 3-form supermultiplet to the general supergravity-matter-Yang-Mills system. Based on the methods of superspace geometry, we identify component fields, establish their supergravity transformations and construct invariant component field actions. Two specific applications are adressed: the appearance of fundamental 3-forms in the context of strong-weak duality and the use of the 3-form supermultiplets to describe effective degrees of freedom relevant to the mechanism of gaugino condensation.