Duality and couplings of 3-form-multiplets in N = 1 supersymmetry

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 Poincaré dual action for massless and massive 3-forms. The resulting target space geometries are Kähler where the respective field variables and superspace couplings are related by a Legendre transformation.

Three-forms in supergravity and flux compactifications

“…This kind of scalar multiplet was introduced in [31] and studied in detail in [38]. For instance [38], studied the relation of these multiplets with other multiplets, in particular, with conventional chiral multiplets. The above simple duality argument explicitly shows how the conventional chiral multiplets and three-form multiplets are related in a manifestly supersymmetric way.…”

Scanning of the supersymmetry breaking scale and the gravitino mass in supergravity

“…The membrane action also contains the coupling of the supergravity three-form H mnp and the matter three-form C mnp to the membranes. Further discussion on three-forms in supersymmetry and supergravity can be found in [27][28][29][30][31][32][33][34]. Here we have to pause and point out that the membrane coupled to the supergravity three-form has a κ-symmetry, while the one coupled to the matter three-form does not.…”

Three-form multiplet and inflation

“…The three-form multiplet in supersymmetry is defined as the real superfield [47][48][49][50][51][52][53] …”

“…Notice that for the purpose of finding the correct on-shell lagrangian and scalar potential, there is a simpler formulation in which S is treated as a standard chiral superfield with D +iF as standard auxiliary fields, no boundary terms are included, but the superpotential of the theory is changed according to [51][52][53] 12) which in our case becomes…”