Proof of all-order finiteness for planar beta-deformed Yang-Mills

TL;DR

This paper proves that a beta-deformed N=4 Yang-Mills theory remains finite at all orders in perturbation theory in the planar limit, demonstrating its conformal invariance despite reduced supersymmetry.

Contribution

It introduces a superspace star-product formulation for the beta-deformed theory and proves its all-order UV finiteness in the planar approximation.

Findings

The beta-deformed theory is conformally invariant in the planar limit.

Green functions are ultraviolet finite to all orders in perturbation theory.

The formulation preserves N=4 light-cone superspace structure despite N=1 supersymmetry.

Abstract

We study a marginal deformation of N=4 Yang-Mills, with a real deformation parameter beta. This beta-deformed model has only N=1 supersymmetry and a U(1)xU(1) flavor symmetry. The introduction of a new superspace star-product allows us to formulate the theory in N=4 light-cone superspace, despite the fact that it has only N=1 supersymmetry. We show that this deformed theory is conformally invariant, in the planar approximation, by proving that its Green functions are ultra-violet finite to all orders in perturbation theory.