On the semiclassical mass of ${\mathbb S}^2$-kinks

TL;DR

This paper calculates the quantum one-loop mass corrections to stable kinks in a massive non-linear ${ m S}^2$-sigma model, using heat kernel and zeta function regularization to handle divergences and comparing exact and asymptotic methods.

Contribution

It provides the first detailed computation of one-loop mass shifts for ${ m S}^2$-kinks using heat kernel/zeta function techniques and compares different regularization approaches.

Findings

Ultraviolet divergences are effectively controlled by heat kernel/zeta function regularization.

Exact and high-temperature asymptotic heat trace methods yield consistent results.

The computed mass shifts enhance understanding of quantum corrections in non-linear sigma models.

Abstract

One-loop mass shifts to the classical masses of stable kinks arising in a massive non-linear ${\mathbb S}^2$-sigma model are computed. Ultraviolet divergences are controlled using the heat kernel/zeta function regularization method. A comparison between the results achieved from exact and high-temperature asymptotic heat traces is analyzed in depth.