Non-planar operator mixing by Brauer 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.