Chern-Simons Couplings and Inequivalent Vector-Tensor Multiplets

TL;DR

This paper explores two distinct off-shell vector-tensor multiplet formulations in N=2 supersymmetry, distinguished by their Chern-Simons couplings, with implications for supersymmetry transformations and dimensional reduction.

Contribution

It demonstrates the existence of two inequivalent vector-tensor multiplet versions with different Chern-Simons couplings and supersymmetry properties, applicable to any number of multiplets.

Findings

One version has quadratic Chern-Simons coupling leading to nonlinear supersymmetry.

Second version maintains linear supersymmetry transformations, related to 6D tensor reduction.

Applicable to arbitrary numbers of vector-tensor multiplets.

Abstract

The off-shell vector-tensor multiplet is considered in an arbitrary background of N=2 vector supermultiplets. We establish the existence of two inequivalent versions, characterized by different Chern-Simons couplings. In one version the vector field of the vector-tensor multiplet is contained quadratically in the Chern-Simons term, which implies nonlinear terms in the supersymmetry transformations and equations of motion. In the second version, which requires a background of at least two abelian vector supermultiplets, the supersymmetry transformations remain at most linear in the vector-tensor components. This version is of the type known to arise from reduction of tensor supermultiplets in six dimensions. Our work applies to any number of vector-tensor multiplets.