On the all-order perturbative finiteness of the deformed N=4 SYM theory

TL;DR

This paper proves that the deformed N=4 SYM theory's chiral propagator remains finite at all orders in perturbation theory for any complex deformation parameter, revealing a new protection mechanism for certain chiral operators.

Contribution

It demonstrates all-order perturbative finiteness of the deformed N=4 SYM theory and introduces a new protection mechanism for chiral operators of dimension three.

Findings

Chiral propagator can be made finite to all orders for any complex deformation parameter.

A new protection mechanism for chiral operators of dimension three is identified.

The all-order form of a specific chiral primary operator is derived from finiteness conditions.

Abstract

We prove that the chiral propagator of the deformed N=4 SYM theory can be made finite to all orders in perturbation theory for any complex value of the deformation parameter. For any such value the set of finite deformed theories can be parametrized by a whole complex function of the coupling constant g. We reveal a new protection mechanism for chiral operators of dimension three. These are obtained by differentiating the Lagrangian with respect to the independent coupling constants. A particular combination of them is a CPO involving only chiral matter. Its all-order form is derived directly from the finiteness condition. The procedure is confirmed perturbatively through order g^6.