Four-loop anomalous dimensions in Leigh-Strassler deformations

TL;DR

This paper calculates four-loop anomalous dimensions in Leigh-Strassler deformations of N=4 super Yang-Mills, providing new insights into operator scaling and confirming conjectures about the rational parts of these dimensions.

Contribution

It presents the first four-loop scalar dilatation operator for Leigh-Strassler deformations, including explicit computations for specific subsectors and comparison with existing conjectures.

Findings

Rational part of anomalous dimensions matches previous conjectures.

Additional zeta(3) terms are found in the four-loop results.

Explicit anomalous dimensions computed for SU(2) and cubic Leigh-Strassler subsectors.

Abstract

We determine the scalar part of the four-loop chiral dilatation operator for Leigh-Strassler deformations of N=4 super Yang-Mills. This is sufficient to find the four-loop anomalous dimensions for operators in closed scalar subsectors. This includes the SU(2) subsector of the (complex) beta-deformation, where we explicitly compute the anomalous dimension for operators with a single impurity. It also includes the "3-string null" operators of the cubic Leigh-Strassler deformation. Our four-loop results show that the rational part of the anomalous dimension is consistent with a conjecture made in arXiv:1108.1583 based on the three-loop result of arXiv:1008.3351 and the N=4 magnon dispersion relation. Here we find additional zeta(3) terms.