Tunneling Through Sphalerons: The O(3) Sigma-Model on a Cylinder

TL;DR

This paper constructs all instantons for the O(3) sigma-model on a cylindrical geometry, revealing that the largest instantons pass through sphalerons and reinterpreting moduli-space to relate scale parameters to boundary conditions.

Contribution

It provides a complete classification of instantons on a cylinder and introduces a novel interpretation linking scale parameters to boundary conditions.

Findings

Largest instantons pass through sphalerons

Reinterpretation of moduli-space connects scale to boundary conditions

Potential insights into the instanton gas divergence

Abstract

We construct all instantons for the \nlsig\ on a cylinder, known not to exist on a finite time interval. We show that the widest instantons go through sphalerons. A re-interpretation of moduli-space transforms the scale parameter $\rho$ to a boundary condition in time. This may give a handle on the $\rho\rightarrow0$ divergent instanton gas.