Operator Mixing and the AdS/CFT correspondence

TL;DR

This paper develops a method to compute operator mixing in N=4 SYM and its string dual, providing explicit results for BMN operators and matching field theory with string theory predictions.

Contribution

It introduces a direct prescription based on superalgebra action for calculating operator mixing in both gauge theory and string theory contexts.

Findings

Derived leading planar quantum corrections for BMN operators in SYM.

Matched string theory predictions with gauge theory results for 2-impurity states.

Predicted higher order quantum corrections to operator mixing.

Abstract

We provide a direct prescription for computing the mixing among gauge invariant operators in N=4 SYM. Our approach is based on the action of the superalgebra on the states of the theory and thus it can be also applied to resolve the mixing in the dual string description. As an example, we focus on the supermultiplet containing the BMN operators with two impurities. On the field theory side, we derive the leading planar quantum corrections to the naive expression of the highest weight state. Then we use the same prescription in the BMN limit of the AdS5xS5 string theory and derive the form of the 2-impurity highest weight state. The string expression matches nicely the SYM result and provides a prediction for the mixing due to higher order quantum corrections in field theory.