Inhomogeneous states in the two-dimensional linear sigma model at large N

Abstract

In this paper we consider inhomogeneous solutions of two-dimensional linear sigma model in the large $N$ limit. These solutions are similar to the ones found recently in the two-dimensional $C{P}^{N}$ sigma model. The solution exists only for some range of coupling constant. We calculate the energy of the solutions as a function of the model parameters and show that it is negative. We analyze the zero modes of the soliton and argue that they can be interpreted as rotational excitations. The case of the nonlinear model at finite temperature is also discussed. The free energy of the inhomogeneous solution is shown to change sign at some critical temperature indicating possible phase transition.