## Abstract

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 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.

Original language | English |
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Article number | 237 |

Journal | Journal of High Energy Physics |

Volume | 2022 |

Issue number | 9 |

DOIs | |

State | Published - 1 Sep 2022 |

## Keywords

- Extended Supersymmetry
- Field Theories in Lower Dimensions
- Renormalization and Regularization
- Supersymmetric Gauge Theory

## ASJC Scopus subject areas

- Nuclear and High Energy Physics