N=2 Supersymmetric Scalar-Tensor Couplings

TL;DR

This paper determines the general coupling of a system of scalars and antisymmetric tensors with at most two derivatives and undeformed gauge transformations for both rigid and local $N=2$ supersymmetry in four-dimensional spacetime. The method uses dualization of hypermultiplets with abelian isometries to tensor multiplets, yielding the general scalar-tensor action with tensors appearing only through their field strengths. The results cover interactions of hyper, tensor and double-tensor multiplets and apply to Calabi–Yau compactifications of Type II supergravities, including a complete dual description of the universal hypermultiplet as a double-tensor multiplet. The work elucidates the geometric structure of the scalar-tensor moduli spaces, with hyperkähler and quaternionic target spaces, and provides explicit Lagrangians and supersymmetry transformation rules useful for instanton analyses and mirror constructions.

Abstract

We determine the general coupling of a system of scalars and antisymmetric tensors, with at most two derivatives and undeformed gauge transformations, for both rigid and local N=2 supersymmetry in four-dimensional spacetime. Our results cover interactions of hyper, tensor and double-tensor multiplets and apply among others to Calabi-Yau threefold compactifications of Type II supergravities. As an example, we give the complete Lagrangian and supersymmetry transformation rules of the double-tensor multiplet dual to the universal hypermultiplet.