# A geometrical point of view on linearized beta-deformations

## TL;DR

This paper offers a super-geometrical perspective on linearized beta-deformations in ${
m extbf{N}}=4$ supersymmetric Yang-Mills theory, linking algebraic structures to geometric interpretations and exploring broader deformation classes.

## Contribution

It introduces a super-geometrical interpretation of beta-deformations using coherent states, extending the understanding of deformations in supersymmetric gauge theories.

## Key findings

- Super-geometrical interpretation of beta-deformations.
- Evaluation of deforming operators on coherent states.
- Potential generalizations to other finite-dimensional deformations.

## Abstract

It is known that the supermultiplet of beta-deformations of ${\cal N}=4$ supersymmetric Yang-Mills theory can be described in terms of the exterior product of two adjoint representations of the superconformal algebra. We present a super-geometrical 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 ${\cal N}=4$ supersymmetric Yang-Mills theory.