Classical and quantum aspects of non-linear sigma models with a squashed sphere target space

TL;DR

This paper explores the classical and quantum properties of non-linear sigma models with a squashed sphere target space, addressing topological defects, discrepancies in expansion methods, and developing a systematic operator product expansion approach.

Contribution

It introduces a systematic operator product expansion at sub-leading order in large N and clarifies discrepancies between different expansion methods.

Findings

Identification of three-dimensional topological defects relevant for magnetic systems

Resolution of the discrepancy between large N and weak coupling expansions

Development of a trans-series expansion for the spinon two-point function with ambiguity cancellation

Abstract

Various aspects of non-linear sigma models with an $SU(N)\times U(1)$ symmetric target space are considered. In the case $N=2$, three-dimensional topological defects are discussed which are relevant for frustrated magnetic systems and which may offer a new perspective on the Skyrme model. An apparent discrepancy between the large $N$ expansion and the weak coupling expansion noted earlier in the literature is reviewed and clarified. A systematic approach to the operator product expansion at sub-leading order in large $N$ is developed and the spinon two-point function is expanded as a trans-series in which all ambiguities in the Borel plane are shown to cancel.