Exact Large R-charge Correlators in ABJM Theory

TL;DR

This paper constructs and analyzes Schur polynomial operators in ABJM theory, providing exact correlators at finite N and in specific backgrounds, revealing nonplanar corrections and resummation techniques.

Contribution

It introduces a class of Schur polynomial operators in ABJM theory and computes their exact correlators, including nonplanar corrections in nontrivial backgrounds.

Findings

Operators are diagonal in free field limit at finite N

Exact multi-point correlators are computed at zero coupling

Nonplanar corrections can be resummed into a 1/(N+M) expansion

Abstract

We construct a class of operators, given by Schur polynomials, in ABJM theory. By computing two point functions at finite $N$ we confirm these are diagonal for this class of operators in the free field limit. We also calculate exact three and multi point correlators in the zero coupling limit. Finally, we consider a particular nontrivial background produced by an operator with an $R$-charge of $O(N^2$. We show that the nonplanar corrections (which can no longer be neglected, even at large $N$) can be resummed to give a $1/(N+M)$ expansion for correlators computed in this background.