Quasi-self-dual Skyrme model

Abstract

A modification of the Skyrme model has been recently proposed, which admits an exact self-dual sector by the introduction of six scalar fields assembled in a symmetric, positive, and invertible $3\ifmmode\times\else\texttimes\fi{}3$ matrix $h$. In this paper we study soft manners of breaking the self-duality of that model. The crucial observation is that the self-duality equations impose distinct conditions on the three eigenvalues of $h$, and on the three fields lying in the orthogonal matrix that diagonalizes $h$. We keep the self-duality equations for the latter, and break those equations associated to the eigenvalues. We perform the breaking by the addition of kinetic and potential terms for the $h$ fields, and construct numerical solutions using the gradient flow method to minimize the static energy. It is also shown that the addition of just a potential term proportional to the determinant of $h$ leads to a model with an exact self-dual sector and with self-duality equations differing from the original ones by just an additional coupling constant.