Renormalization of the Nonlinear O(3) Model with Theta-Term

TL;DR

This paper investigates how the topological term in the 2D nonlinear O(3) model behaves under renormalization, revealing finite multiplicative renormalization in the infrared using the Functional Renormalization Group and index theorem techniques.

Contribution

It introduces a novel approach to renormalize the topological charge by treating it as a limit of a more general operator and employs a Clifford algebra representation to analyze zero modes.

Findings

Finite multiplicative renormalization in the infrared.

A new representation of the Clifford algebra for zero mode analysis.

Application of the index theorem to the nonlinear O(3) model.

Abstract

The renormalization of the topological term in the two-dimensional nonlinear O(3) model is studied by means of the Functional Renormalization Group. By considering the topological charge as a limit of a more general operator, it is shown that a finite multiplicative renormalization occurs in the extreme infrared. In order to compute the effects of the zero modes, a specific representation of the Clifford algebra is developed which allows to reformulate the bosonic problem in terms of Dirac operators and to employ the index theorem.