BPS and non-BPS kinks in a massive non-linear S^2-sigma model

TL;DR

This paper analyzes the stability, quantum corrections, and BPS versus non-BPS nature of kinks in a massive non-linear S^2-sigma model, combining spectral analysis, first-order equations, and quantum mass shift calculations.

Contribution

It introduces a method to distinguish BPS from non-BPS kinks and computes their quantum mass shifts using the Cahill-Comtet-Glauber formula.

Findings

BPS and non-BPS kinks are characterized and distinguished.

Quantum one-loop mass shifts are calculated for the kinks.

Non-topological kinks are shown to be unstable via Morse index theorem.

Abstract

The stability of the kinks of the non-linear ${\mathbb S}^2$-sigma model discovered in Phys. Rev. Lett. 101(2008)131602 is discussed from several points of view. After a direct estimation of the spectra of the second-order fluctuation operators around topological kinks, first-order field equations are proposed to distinguish between BPS and non-BPS kinks. The one-loop mass shifts caused by quantum fluctuations around the topological kinks are computed using the Cahill-Comtet-Glauber formula proposed in Phys. Lett. 64B(1976)283. The (lack of) stability of the non-topological kinks is unveiled by application of the Morse index theorem. These kinks are identified as non-BPS states and the interplay between instability and supersymmetry is explored.