Self-Dual Vector Multiplet in 3D with Gauged Scale Covariance

TL;DR

This paper develops a novel 3D N=1 self-dual massive vector multiplet with gauged scale covariance, introducing new interactions and exploring spontaneous symmetry breaking without a Lagrangian framework.

Contribution

It presents the first construction of a self-dual vector multiplet with gauged scale covariance in three dimensions, including Dirac-Born-Infeld interactions and scalar couplings.

Findings

Gauged scale covariance is achievable without supergravity.

The system admits Dirac-Born-Infeld type interactions.

Spontaneous breaking of scale covariance is possible via superpotential.

Abstract

We present non-trivial interactions of N=1 self-dual massive vector multiplet in three-dimensions, with gauged scale covariance. Our multiplets are a vector multiplet (A_\mu, \lambda) and a gauge multiplet (B_\mu, \chi), where the latter is used for the gauging of the scale covariance of the former. Due tothe absence of supergravity, this system has no lagrangian formulation, but has only a set of field equations. The gauge multiplet can also have Dirac-Born-Infeld type interactions, even in the presence of the massive self-dual vector multiplet. As a by-product, we also show that scale covariant couplings are possible for scalar multiplet. We also try a mechanism of spontaneous breaking of scale covariance by introducing a superpotential for scalar multiplets.