Vector operators in the BMN correspondence

TL;DR

This paper computes anomalous dimensions of mixed scalar-vector BMN operators at planar and torus levels, confirming consistency with the BMN conjecture and exploring implications for the gauge/string correspondence in pp-wave backgrounds.

Contribution

It provides the first calculation of anomalous dimensions for mixed scalar-vector BMN operators at both planar and torus levels, confirming theoretical predictions.

Findings

Anomalous dimensions match those of scalar BMN operators.

Agreement at torus level explained by supersymmetry arguments.

Results support the BMN correspondence in string theory.

Abstract

We consider a BMN operator with one scalar, phi, and one vector, D_{m}Z, impurity field and compute the anomalous dimension both at planar and torus levels. This "mixed" operator corresponds to a string state with two creation operators which belong to different SO(4) sectors of the background. The anomalous dimension at both levels is found to be the same as the scalar impurity BMN operator. At planar level this constitutes a consistency check of BMN conjecture. Agreement at the torus level can be explained by an argument using supersymmetry and supression in the BMN limit. The same argument implies that a class of fermionic BMN operators also have the same planar and torus level anomalous dimensions. Implications of the results for the map from N=4 SYM theory to string theory in the pp-wave background are discussed.