Instantons and the fixed point topological charge in the two-dimensional O(3) sigma-model

TL;DR

This paper introduces a defect-free fixed point topological charge for the 2D O(3) sigma-model, uses it to measure topological susceptibility, and discusses its physical relevance, with potential applications to other theories.

Contribution

It defines a new fixed point topological charge free of defects and demonstrates its use in measuring susceptibility in the sigma-model.

Findings

Topological susceptibility may not be a physical quantity in the model.

The method can be applied to other asymptotically free theories.

The fixed point charge avoids topological defects.

Abstract

We define a fixed point topological charge for the two-dimensional O(3) lattice sigma-model which is free of topological defects. We use this operator in combination with the fixed point action to measure the topological susceptibility for a wide range of correlation lengths. The results strongly suggest that it is not a physical quantity in this model. The procedure, however, can be applied to other asymptotically free theories as well.