Duality and Couplings of 3-Form-Multiplets in N=1 Supersymmetry

TL;DR

This work analyzes 3-form gauge fields within four-dimensional ${N=1}$ supersymmetry, constructing both the renormalizable and non-renormalizable sigma-model actions for massless and massive 3-form multiplets and their Poincaré duals. It establishes Kahler target-space geometry and demonstrates Legendre-transform relations between original and dual variables, including careful treatment of supersymmetric boundary terms that generate a cosmological constant. The study extends to couplings with chiral multiplets, deriving SUSY-breaking conditions and mass spectra, and systematically maps how dual descriptions interchange 3-forms for real or complex scalars depending on the mass regime. Together, these results provide a comprehensive framework for incorporating 3-forms in ${N=1}$ effective actions relevant to string compactifications and flux backgrounds.

Abstract

In this paper we study 3-form gauge fields in four-dimensional N=1 supersymmetric theories. We give the sigma model action together with its Poincare dual action for massless and massive 3-forms. The resulting target space geometries are Kahler where the respective field variables and superspace couplings are related by a Legendre transformation.