Supersymmetric Galilean Electrodynamics

TL;DR

This paper introduces a non-linear sigma model for 2+1 dimensional $ ext{N}=2$ supersymmetric Galilean Electrodynamics, analyzing its renormalization properties and identifying a conformal manifold of fixed points.

Contribution

It constructs a renormalizable non-linear sigma model for supersymmetric Galilean Electrodynamics and explores its quantum properties and conformal invariance.

Findings

The theory is non-renormalizable in its simplest form.

Infinite supersymmetric, gauge-invariant terms are generated quantum mechanically.

Renormalizability is achieved through a generalized sigma model with marginal couplings.

Abstract

In 2+1 dimensions, we propose a renormalizable non-linear sigma model action which describes the $\mathcal{N}=2$ supersymmetric generalization of Galilean Electrodynamics. We first start with the simplest model obtained by null reduction of the relativistic Abelian $\mathcal{N}=1$ supersymmetric QED in 3+1 dimensions and study its renormalization properties directly in non-relativistic superspace. Despite the existence of a non-renormalization theorem induced by the causal structure of the non-relativistic dynamics, we find that the theory is non-renormalizable. Infinite dimensionless, supersymmetric and gauge-invariant terms, which combine into an analytic function, are generated at quantum level. Renormalizability is then restored by generalizing the theory to a non-linear sigma model where the usual minimal coupling between gauge and matter is complemented by infinitely many marginal couplings driven by a dimensionless gauge scalar and its fermionic superpartner. Superconformal invariance is preserved in correspondence of a non-trivial conformal manifold of fixed points where the theory is gauge-invariant and interacting.