Four-loop anomalous dimensions in Leigh–Strassler deformations

Abstract

We determine the scalar part of the four-loop chiral dilatation operator for Leigh–Strassler deformations of 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) β-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 Minahan (2011 J. High Energy Phys. JHEP12(2011)093) based on the three-loop result of Sieg (2011 Phys. Rev. D 84 045014) and the magnon dispersion relation. Here, we find additional ζ(3) terms.