On the perturbative chiral ring for marginally deformed N=4 SYM theories

TL;DR

This paper investigates the structure of the chiral ring in marginally deformed N=4 SYM theories, providing a perturbative method to identify protected operators and analyzing specific deformations up to three loops.

Contribution

It introduces a new perturbative procedure to determine protected chiral operators in deformed N=4 SYM theories using the effective superpotential, extending to complex Leigh-Strassler deformations.

Findings

Determined the quantum structure of operators in the beta-deformed theory up to three loops.

Extended the analysis to Leigh-Strassler deformations for sectors up to two loops.

Provided insights into the properties and structure of the chiral ring in these theories.

Abstract

For \cal{N}=1 SU(N) SYM theories obtained as marginal deformations of the \cal{N}=4 parent theory we study perturbatively some sectors of the chiral ring in the weak coupling regime and for finite N. By exploiting the relation between the definition of chiral ring and the effective superpotential we develop a procedure which allows us to easily determine protected chiral operators up to n loops once the superpotential has been computed up to (n-1) order. In particular, for the Lunin-Maldacena beta-deformed theory we determine the quantum structure of a large class of operators up to three loops. We extend our procedure to more general Leigh-Strassler deformations whose chiral ring is not fully understood yet and determine the weight-two and weight-three sectors up to two loops. We use our results to infer general properties of the chiral ring.