The Dark Side of Double-Tensor Multiplets

TL;DR

This paper investigates free double-tensor multiplets in N=2 supersymmetry, revealing their on-shell closure of supersymmetry algebra and inherent non-locality in superspace, while maintaining a Lagrangian formulation.

Contribution

It provides a detailed analysis of double-tensor multiplets in superspace and spacetime, highlighting their non-local features and the role of Hodge-dual scalars in superspace cohomology.

Findings

Supersymmetry algebra closes only on-shell for these multiplets.

Superspace cohomology requires dual scalars to describe tensor super-fields.

The theory exhibits inherent non-locality even in the free case.

Abstract

We explore the properties of a set of free double-tensor multiplets in $N=2$ supersymmetry, focusing on their behavior within rigid superspace. These multiplets can be obtained from hypermultiplets by Hodge-dualizing half of their scalars, and feature an off-shell matching of bosonic and fermionic degrees of freedom. Despite this fact, the supersymmetry algebra results to close only on-shell. Our analysis is conducted both in superspace, using the geometric (rheonomic) approach, and in spacetime, comparing how our results are obtained in the two approaches. Notably, the cohomology of superspace requires that the scalars Hodge-dual to the antisymmetric tensors crucially contribute to the superspace description of the tensors super-field strengths. This shows an inherent non-locality of the theory, already in the free case, which however does not forbid a Lagrangian description.