The tensor multiplet in loop space

TL;DR

This paper reformulates the abelian tensor multiplet on curved spacetime into a cohomological form, maps it to loop space, and extends the framework to nonabelian gauge groups, deriving equations of motion via supersymmetry closure.

Contribution

It introduces a cohomological reformulation of the tensor multiplet in curved spacetime and extends the loop space approach to nonabelian gauge groups.

Findings

Derived equations of motion in loop space for abelian tensor multiplet.

Extended the formalism to include nonabelian gauge groups.

Closed supersymmetry variations to obtain fermionic equations of motion.

Abstract

We reformulate the abelian tensor multiplet on a curved spacetime with at least two supercharges in a cohomological form where all the bosonic and fermionic fields become tensor fields. These tensor fields are rewritten as fields in loop space by a transgression map. There are two lightlike conformal Killing vectors. By decomposing the spacetime tensor fields in transverse and parallel components to these Killing vectors, we obtain the equations of motion in loop space by closing the supersymmetry variations on-shell. We generalize to nonabelian gauge groups. By closing supersymmetry variations we obtain nonabelian fermionic equations of motion in loop space.