Cut-and-join operators and N=4 super Yang-Mills

TL;DR

This paper investigates the structure of multi-trace operators in N=4 super Yang-Mills, identifying how cut-and-join operators describe non-planar corrections and providing new counting methods for protected operators.

Contribution

It introduces a novel approach to understanding multi-trace structures and non-planar corrections using cut-and-join operators and Weyl group techniques.

Findings

Identified compatible multi-trace structures with symmetry group representations

Derived 1/N corrections for quarter-BPS operators

Developed a new counting method for chiral ring operators

Abstract

We show which multi-trace structures are compatible with the symmetrisation of local operators in \cN=4 super Yang-Mills when they are organised into representations of the global symmetry group. Cut-and-join operators give the non-planar expansion of correlation functions of these operators in the free theory. Using these techniques we find the 1/N corrections to the quarter-BPS operators which remain protected at weak coupling. We also present a new way of counting these chiral ring operators using the Weyl group S_N.