On nonanticommutative N=2 sigma-models in two dimensions

TL;DR

This paper explores nonanticommutative deformations of N=2 two-dimensional Euclidean sigma models, revealing simple Lagrangian modifications, geometric interpretations as target space fuzziness, and intriguing supersymmetry algebra extensions upon continuation to Lorentzian signature.

Contribution

It introduces a novel class of deformations for N=2 sigma models, linking algebraic, geometric, and supersymmetric structures in a unified framework.

Findings

Deformation described by simple modifications of Zumino's Lagrangian and superpotential.

Geometric interpretation as target space fuzziness controlled by auxiliary fields.

Deformed supersymmetry algebra exhibits a central extension upon Lorentzian continuation.

Abstract

We study nonanticommutative deformations of N=2 two-dimensional Euclidean sigma models. We find that these theories are described by simple deformations of Zumino's Lagrangian and the holomorphic superpotential. Geometrically, this deformation can be interpreted as a fuzziness in target space controlled by the vacuum expectation value of the auxiliary field. In the case of nonanticommutative deformations preserving Euclidean invariance, we find that a continuation of the deformed supersymmetry algebra to Lorentzian signature leads to a rather intriguing central extension of the ordinary (2,2) superalgebra.