Topics in Nonlinear Sigma Models in D=3

TL;DR

This paper explores the perturbative and non-perturbative features of three-dimensional nonlinear sigma models, highlighting UV divergence cancellations in supersymmetric cases and analyzing soliton dynamics in noncommutative extensions.

Contribution

It provides new insights into UV divergence cancellations in 3D supersymmetric NLSM and investigates soliton behavior in noncommutative models.

Findings

UV divergences cancel in extended supersymmetric NLSM in low orders of 1/n expansion

Analysis of BPS soliton dynamics in noncommutative CP(n) model

Discussion of non-BPS solution dynamics

Abstract

Nonlinear sigma models (NLSM) in d=3 have many interesting and non-trivial features, which were explored poorly in contrast with NLSM in d=2 and d=4. We present a few results from our study of the perturbative and non-perturbative properties of three-dimensional (3D) NLSM. i) We have shown that cancellation of ultra-violet (UV) divergences takes place in 3D extended (N=2,4) supersymmetric NLSM in low orders of the 1/n expansion. ii) We consider noncommutative extension of the 3D CP(n) model, and study low-energy dynamics of BPS solitons in this model. We also discuss briefly dynamics of non-BPS solutions.