Structure constants of heavy operators in ABJM/ABJ Theory

TL;DR

This paper extends efficient correlation function computation methods from ${ m f ext{N}=4}$ super Yang-Mills to ABJM and ABJ theories, introducing integral representations that facilitate analysis and highlight holographic relevance.

Contribution

It introduces a novel integral representation for projection operators in ABJM/ABJ theory, extending previous methods and emphasizing their holographic significance.

Findings

Effective computation of correlation functions in ABJM/ABJ theories.

Integral representation based on character orthogonality.

Loop expansion parameter identified as 1/N.

Abstract

Efficient and powerful approaches to the computation of correlation functions involving determinant, sub-determinant and permanent operators, as well as traces, have recently been developed in the setting of ${\cal N}=4$ super Yang-Mills theory. In this article we show that they can be extended to ABJM and ABJ theory. After making use of a novel identity which follows from character orthogonality, an integral representation of certain projection operators used to define Schur polynomials is given. This integral representation provides an effective description of the correlation functions of interest. The resulting effective descriptions have ${1\over N}$ as the loop counting parameter, strongly suggesting their relevance for holography.