Interpretation and further properties of general classical CPn−1 solutions

Abstract

We present arguments suggesting that non-(anti) self-dual classical solutions to the equations of motion of the euclidean CP n −1 model can be interpreted as unstable non-interacting mixtures of instantons and anti-instantons. Fermionic modes in the background of these solutions are discussed. We determine the modes explicitly for the case of an embedded O(3) solution and point out that they give rise to a non-trivial illustration of the Atiyah-Singer index theorem.