N=1 Wess Zumino Model in d=3 at zero and finite temperature

TL;DR

This paper derives supersymmetric RG flow equations for the 3D Wess-Zumino model at zero and finite temperature, analyzing phase transitions, symmetry restoration, and dimensional reduction effects.

Contribution

It provides the first derivation of supersymmetric RG flow equations for the 3D Wess-Zumino model at finite temperature and maps its phase diagram.

Findings

Identifies the phase transition line separating supersymmetric and non-supersymmetric phases.

Shows dimensional reduction from 3D to 2D at finite temperature in the infrared.

Demonstrates the Stefan-Boltzmann law for pressure above the Z2 phase transition.

Abstract

Supersymmetric renormalization group (RG) flow equations for the effective superpotential of the three-dimensional Wess-Zumino model are derived at zero and non-zero temperature. This model with fermions and bosons interacting via a Yukawa term possesses a supersymmetric analogue of the Wilson-Fisher fixed-point. At zero temperature we determine the phase-transition line in coupling-constant space separating the supersymmetric from the non-supersymmetric phase. At finite temperature we encounter dimensional reduction from 3 to 2 dimensions in the infrared regime. We determine the finite-temperature phase diagram for the restoration of the global $Z_2$-symmetry and show that for temperatures above the $Z_2$ phase transition the pressure obeys the Stefan-Boltzmann law of a gas of massless bosons in 2+1 dimensions.