Non-anticommutative solitons

TL;DR

This paper explores how non-anticommutative deformations affect supersymmetric sigma models in 2+1 dimensions, leading to new soliton solutions with additional spin features and altered properties compared to traditional models.

Contribution

It introduces a non-anticommutative deformation using Clifford algebra, constructs new soliton solutions, and analyzes their unique properties and differences from previous models.

Findings

Deformation introduces spin-1/2 degrees of freedom in solitons.

Constructs static CP^1 and scattering U(2) solitons with new features.

Abelian BPS solutions have infinite action, unlike in the Moyal case.

Abstract

Certain supersymmetric sigma models in 2+1 dimensions feature multi-soliton solutions, with and without scattering. We subject these systems to a non-anticommutative deformation by replacing the Grassmann algebra of the odd superspace coordinates with a Clifford algebra. Static CP^1 and scattering U(2) solitons are constructed and carry an additional spin-1/2 degree of freedom due to the deformation. Abelian BPS solutions exist as well but have infinite action, in contrast to the Moyal case.