A basis for large operators in N=4 SYM with orthogonal gauge group

TL;DR

This paper develops new techniques to analyze large operators in SO(N) gauge theory, extending the understanding of correlation functions beyond planar diagrams and providing exact free field correlators.

Contribution

It introduces a group representation theory approach to define and diagonalize large operators in SO(N) gauge theory, generalizing Schur polynomials for this setting.

Findings

Exact two-point functions for large operators in SO(N) gauge theory

Operators diagonalize the two-point function in the free limit

Framework for computing correlators in the trace basis

Abstract

We develop techniques to study the correlation functions of "large operators" whose bare dimension grows parametrically with N, in SO(N) gauge theory. We build the operators from a single complex matrix. For these operators, the large N limit of correlation functions is not captured by summing only the planar diagrams. By employing group representation theory we are able to define local operators which generalize the Schur polynomials of the theory with gauge group U(N). We compute the two point function of our operators exactly in the free field limit showing that they diagonalize the two point function. We explain how these results can be used to obtain the exact free field answers for correlators of operators in the trace basis.