On the existence of localized solutions in nonlinear chiral theories

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Abstract
We study the existence of localized solutions to theories based on Weinberg’s nonlinear realization of chiral SU(2) ⊗SU(2). The analysis is done by using specific variations of the action integral and then checking the ensuing global conditions. The following cases are studied: (i) π fields only and without time dependence, (ii) π fields with simple time dependence, (iii) π fields coupled to gauge fields, (iv) the above with certain chiral symmetry breaking potentials. We find that only in certain special cases could there be localized solutions. In most cases the intrinsic nonlinearity of the system does not seem to be enough to guarantee their existence.