Abstract
We present a duality procedure that relates conventional four-dimensional matter-coupled mathcal{N}=1 supergravities to dual formulations in which auxiliary fields are replaced by field strengths of gauge three-forms. The duality promotes specific coupling constants appearing in the superpotential to vacuum expectation values of the field strengths. We then apply this general duality to type IIA string compactifications on Calabi–Yau orientifolds with RR fluxes. This gives a new supersymmetric formulation of the corresponding effective four-dimensional theories which includes gauge three-forms.
Highlights
We present a duality procedure that relates conventional four-dimensional matter-coupled N = 1 supergravities to dual formulations in which auxiliary fields are replaced by field strengths of gauge three-forms
The question is : does there exist an alternative supersymmetric formulation of the effective theory with a set of pairs of gauge three-forms ( A3A, A3A) in which the coupling constants eA and m B are promoted to vacuum expectation values of the field strengths F4A = d A3A and F4A = d A3A? Note that this procedure is a certain kind of duality transformation that trades coupling constants for gauge three-forms, which do not carry propagating degrees of freedom in four dimensions
The new formulation will be obtained by a supersymmetric duality transformation, which modifies the structure of the chiral multiplets A, substituting their scalar complex auxiliary fields F A or just the real parts thereof with a combination of the field strengths F4A and F4A
Summary
We explain how the dualization procedure works in the case of rigid N = 1 supersymmetric theories. In the simplest case of constant GAB in (1.1), it will produce known variants of off-shell chiral multiplets, whose auxiliary fields are replaced by the field strength of one or two gauge three-forms. We will refer to these chiral multiplets as single and double three-form multiplets, respectively. In the case of generic GAB( ), the dualization will provide a generalization of these off-shell three-form multiplets
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