Non-anti-commutative deformation of complex geometry

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.

contribution to the International Workshop on Noncommutative Geometry and Physics, November 1-4, 2005, Sendai, Japan; 17 pages, LaTeX