Bifurcation and pattern changing with two real scalar fields

TL;DR

This paper investigates bifurcation and pattern changes in models with two real scalar fields, analyzing domain wall tensions and their implications for cosmological domain wall problems.

Contribution

It introduces a reduction in independent parameters for models with superpotentials and explores bifurcation effects on domain wall networks.

Findings

Reduced parameter space to 4 coefficients in superpotential models

Computed tensions for BPS and non-BPS domain walls

Illustrated bifurcation effects on domain wall patterns

Abstract

This work deals with bifurcation and pattern changing in models described by two real scalar fields. We consider generic models with quartic potentials and show that the number of independent polynomial coefficients affecting the ratios between the various domain wall tensions can be reduced to 4 if the model has a superpotential. We then study specific one-parameter families of models and compute the wall tensions associated with both BPS and non-BPS sectors. We show how bifurcation can be associated to modification of the patterns of domain wall networks and illustrate this with some examples which may be relevant to describe realistic situations of current interest in high energy physics. In particular, we discuss a simple solution to the cosmological domain wall problem.