Off-shell N=2 tensor supermultiplets

TL;DR

This paper develops a comprehensive calculus for N=2 tensor supermultiplets, enabling the construction of supergravity Lagrangians, dualities, and higher-derivative couplings, with applications to quaternion-Kahler manifolds and the c-map.

Contribution

It introduces a new multiplet calculus for N=2 tensor supermultiplets, including higher-derivative couplings and an off-shell c-map, expanding the tools for supergravity model building.

Findings

Reproduces known couplings for rigid supersymmetry.

Derives supergravity Lagrangians with vector, tensor, and hypermultiplets.

Classifies 4D quaternion-Kahler manifolds with two isometries.

Abstract

A multiplet calculus is presented for an arbitrary number n of N=2 tensor supermultiplets. For rigid supersymmetry the known couplings are reproduced. In the superconformal case the target spaces parametrized by the scalar fields are cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant potentials, subject to certain constraints. The coupling to conformal supergravity enables the derivation of a large class of supergravity Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing the tensor fields into scalars leads to hypermultiplets with hyperkahler or quaternion-Kahler target spaces with at least n abelian isometries. It is demonstrated how to use the calculus for the construction of Lagrangians containing higher-derivative couplings of tensor multiplets. For the application of the c-map between vector and tensor supermultiplets to Lagrangians with higher-order derivatives, an off-shell version of this map is proposed. Various other implications of the results are discussed. As an example an elegant derivation of the classification of 4-dimensional quaternion-Kahler manifolds with two commuting isometries is given.