General classical solutions in the noncommutative CP^(N-1) model

TL;DR

This paper constructs explicit classical solutions for the noncommutative CP^(N-1) model in two dimensions, demonstrating their integer action and topological charge, and verifies the index theorem with solutions to the Dirac equation.

Contribution

It provides the first explicit construction of general classical solutions in the noncommutative CP^(N-1) model, confirming their topological properties and the index theorem.

Findings

Solutions have integer action and topological charge.

Explicit solutions to the Dirac equation are provided.

The index theorem is verified in this noncommutative setting.

Abstract

We give an explicit construction of general classical solutions for the noncommutative CP^(N-1) model in two dimensions, showing that they correspond to integer values for the action and topological charge. We also give explicit solutions for the Dirac equation in the background of these general solutions and show that the index theorem is satisfied.