Supergraph techniques for D=3,N=1 broken supersymmetric theories

TL;DR

This paper extends supergraph techniques to broken supersymmetric theories in three dimensions and demonstrates their use by calculating the effective potential in SQED3, revealing gauge symmetry breaking without supersymmetry breaking.

Contribution

The paper introduces supergraph methods applicable to broken supersymmetric gauge theories in D=3, providing a new computational approach for analyzing such models.

Findings

Supersymmetry remains unbroken at the potential's minimum.

Gauge symmetry is dynamically broken, leading to gauge superfield mass.

Two-loop effective potential calculated using tadpole and vacuum bubble methods.

Abstract

We enlarge the usual D=3 N=1 supergraph techniques to include the case of (explicitly or spontaneously) broken supersymmetric gauge theories. To illustrate the utility of these techniques, we calculate the two-loop effective potential of the SQED3 by using the tadpole and the vacuum bubble methods. In these methods, to investigate the possibility of supersymmetry breaking, the superfields must be shifted by $\theta$ dependent classical superfields (vacuum expectation values), what implies in the explicit breakdown of supersymmetry in the intermediate steps of the calculation. Nevertheless, after studying the minimum of the resulting effective potential, we find that supersymmetry is conserved, while gauge symmetry is dynamically broken, with a mass generated for the gauge superfield.