Classical solutions of non-linear σ-models and their quantum fluctuations

Abstract

I study the properties of O(N) and CPⁿ⁻¹ non-linear σ-MOELS in the two dimensional Euclidean space. All classical solutions of the equations of motion can be characterized and in the CPⁿ⁻¹ model they can be expressed in a simple and explicit way in terms of holomorphic vectors. The topological winding number and the action of the general CPⁿ⁻¹ solution can be evaluated and the latter turns out always to be an integer multiple of 2π. I further discuss the stability of the solutions and the problem of one-loop calculations of quantum fluctuations around classical solutions.