Thermal Evolution of the Non Supersymmetric Metastable Vacua in N=2 SU(2) SYM Softly Broken to N=1

TL;DR

This paper investigates the thermal stability of metastable non-supersymmetric vacua in N=2 SU(2) gauge theories softly broken to N=1, analyzing conditions under which the universe can settle in these vacua during cooling.

Contribution

It demonstrates how high-temperature corrections affect metastable vacua and identifies conditions for their stability in the early universe.

Findings

Metastable vacua can be stable at high temperatures if certain conditions are met.

Corrections from BPS dyons can destabilize metastable vacua at high temperatures.

The universe can settle in metastable vacua if the superpotential is sufficiently large and the vacuum is in the strongly coupled region.

Abstract

It has been shown that four dimensional N=2 gauge theories, softly broken to N=1 by a superpotential term, can accommodate metastable non-supersymmetric vacua in their moduli space. We study the SU(2) theory at high temperatures in order to determine whether a cooling universe settles in the metastable vacuum at zero temperature. We show that the corrections to the free energy because of the BPS dyons are such that may destroy the existence of the metastable vacuum at high temperatures. Nevertheless we demonstrate the universe can settle in the metastable vacuum, provided that the following two conditions are hold: first the superpotential term is not arbitrarily small in comparison to the strong coupling scale of the gauge theory, and second the metastable vacuum lies in the strongly coupled region of the moduli space.