Supersymmetric Galilean Electrodynamics

In 2+1 dimensions, we propose a renormalizable non-linear sigma model action which describes the N = 2 supersymmetric generalization of Galilean Electrodynamics. We first start with the simplest model obtained by null reduction of the relativistic Abelian 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 nonrenormalizable 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.

Automated summary

In this paper, we propose a renormalizable non-linear sigma model action that describes the relationship between Galilean Electrodynamics and N = 2 supersymmetry. By studying the model directly in non-relativistic superspace, we find that it is nonrenormalizable, but this issue is resolved by introducing infinitely many marginal couplings. The superconformal invariance is also preserved.