Non-planar operator mixing by Brauer representations

TL;DR

This paper investigates how the dilatation operator acts on operators built from the walled Brauer algebra, revealing a structured approach to non-planar operator mixing using algebraic representations.

Contribution

It introduces a framework to analyze non-planar operator mixing via irreducible representations of the walled Brauer algebra, emphasizing the significance of a key integer parameter.

Findings

Operator mixing expressed through algebraic irreducible representations

Non-planar corrections fully incorporated in the analysis

Identification of a key integer parameter influencing representations

Abstract

We study the action of the dilatation operator on the basis of local operators constructed from the elements of the walled Brauer algebra, with non-planar corrections fully taken into account. We will see that the operator mixing can be neatly expressed in terms of the irreducible representations of the algebra. In particular we focus on a role of the integer that determines the number of boxes in the representations.