On dynamical mass generation in three dimensional supersymmetric U(1) gauge field theory

TL;DR

This paper explores the non-perturbative infrared behavior of three-dimensional supersymmetric U(1) gauge theories, providing evidence for dynamical mass generation in N=1 models and clarifying gauge dependence issues in N=2 models.

Contribution

It offers a detailed analysis of dynamical mass generation using superfield formalism and clarifies the gauge dependence of mass generation in N=2 supersymmetric models.

Findings

Evidence for gauge-independent dynamical mass in N=1 models

Refinement of gauge dependence argument in N=2 models

Critical behavior observed in wavefunction renormalization

Abstract

We investigate and contrast the non-perturbative infra red structure of N=1 and N=2 supersymmetric non-compact U(1) gauge field theory in three space-time dimensions with N matter flavours. We study the Dyson-Schwinger equations in a general gauge using superfield formalism; this ensures that supersymmetry is kept manifest, though leads to spurious infra red divergences which we have to avoid carefully. In the N=1 case the superfield formalism allows us to choose a vertex which satisfies the U(1) Ward identity exactly, and we find the expected critical behaviour in the wavefunction renormalization and strong evidence for the existence of a gauge independent dynamically generated mass, but with no evidence for a critical flavour number. We study the N=2 model by dimensional reduction from four dimensional N=1 electrodynamics, and we refine the old gauge dependence argument that there is no dynamical mass generation. We recognize that the refinement only holds after dimensional reduction.