# Wess-Zumino term by Vacuum Overlap Formula

## TL;DR

This paper investigates the lattice regularization of the Wess-Zumino term in two-dimensional SU(2) models, demonstrating correct continuum behavior perturbatively and revealing nonperturbative properties like Gaussian distribution and sharp crossover effects.

## Contribution

It provides a nonperturbative analysis of the vacuum overlap formula for the Wess-Zumino term, highlighting its behavior in different coupling regimes and the impact of species doublers.

## Key findings

- Perturbatively reproduces the Wess-Zumino term in the continuum limit.
- Nonperturbatively shows a sharp Gaussian distribution in the scaling region.
- Identifies a sharp crossover from strong to weak coupling regimes.

## Abstract

We examine the vacuum overlap formula for the two-dimensional SU(2) Wess-Zumino term in lattice regularization. Perturbatively it reproduces the Wess-Zumino term correctly in the continuum limit and yields the IR fixed point in the beta function of the chiral model. Nonperturbatively it shows a sharp Gaussian distribution for the SU(2) chiral field configurations in the scaling region, where smooth configurations dominate even in the symmetric phase due to asymptotic freedom. Crossover is sharp from the strong coupling region where the Wess-Zumino term fluctuates hard and the species doublers' contribution is suspected to affect it.