Conformal Dimensions of Two-Derivative BMN Operators

TL;DR

This paper calculates the anomalous dimensions of two-derivative BMN operators at planar level, revealing similarities with scalar impurity cases but highlighting unique computational differences due to derivative impurities.

Contribution

It provides the first detailed computation of anomalous dimensions for two-derivative BMN operators, showing their equivalence to scalar impurity results despite different methods.

Findings

Anomalous dimensions match those of scalar impurities

Distinct computational approach due to overlap with background field

Results confirm universality of anomalous dimensions across impurity types

Abstract

We compute the anomalous dimensions of BMN operators with two covariant derivative impurities at the planar level up to first order in the effective coupling lambda'. The result equals those for two scalar impurities as well as for mixed scalar and vector impurities given in the literature. Though the results are the same, the computation is very different from the scalar case. This is basically due to the existence of a non-vanishing overlap between the derivative impurity and the ``background'' field Z. We present details of these differences and their consequences.