Duality in Fuzzy Sigma Models

TL;DR

This paper explores BPS solitons in fuzzy sigma models on fuzzy spheres, revealing their quantized nature as Bott projectors and extending to supersymmetric cases, thus advancing understanding of noncommutative field theories.

Contribution

It introduces the concept of fuzzy BPS solitons as quantized Bott projectors and constructs explicit solutions, extending previous work on fuzzy sigma models.

Findings

Fuzzy BPS solitons are quantized Bott projectors.

Explicit construction of fuzzy BPS solitons provided.

Supersymmetric versions derived from existing frameworks.

Abstract

Nonlinear `sigma' models in two dimensions have BPS solitons which are solutions of self- and anti-self-duality constraints. In this paper, we find their analogues for fuzzy sigma models on fuzzy spheres which were treated in detail by us in earlier work. We show that fuzzy BPS solitons are quantized versions of `Bott projectors', and construct them explicitly. Their supersymmetric versions follow from the work of S. Kurkcuoglu.