Non-anti-commutative deformation of complex geometry

TL;DR

This paper reviews the connection between supersymmetry and complex geometry, and discusses recent advances in non-anti-commutative deformations within supersymmetric non-linear sigma-models, highlighting their mathematical and physical implications.

Contribution

It introduces and analyzes non-anti-commutative deformations in supersymmetric sigma-models, expanding the understanding of geometry and noncommutativity in theoretical physics.

Findings

Established links between extended supersymmetry and complex geometry.

Explored non-anti-commutative deformations in supersymmetric models.

Discussed implications for geometry, supersymmetry, and noncommutativity.

Abstract

The well known relation between extended supersymmetry and complex geometry in the non-linear sigma-models is reviewed, and some recent developments related to the introduction of the non-anti-commutativity, in the context of the supersymmetric non-linear sigma-models formulated in extended superspace, are discussed. This contribution is suitable for both physicists and mathematicians interesting in the interplay between geometry, supersymmetry and noncommutativity.