A geometrical point of view on linearized beta-deformations

Abstract

It is known that the supermultiplet of beta-deformations of N = 4 supersymmetric Yang-Mills theory can be described in terms of the exterior product of two adjoint representations of the superconformal algebra. We present a supergeometrical interpretation of this fact, by evaluating the deforming operator on some special coherent states in the space of supersingletons. We also discuss generalization of this approach to other finite-dimensional deformations of the N = 4 supersymmetric Yang-Mills theory.