Two-Point Functions in ABJM Matrix Model

TL;DR

This paper introduces and analyzes non-trivial two-point functions of super Schur polynomials in the ABJM matrix model, revealing simple relations with one-point functions and exploring BPS index splitting.

Contribution

It presents the first exact evaluation of two-point functions in the ABJM matrix model using the Fermi gas formalism, uncovering new relations and insights.

Findings

Two-point functions relate to one-point functions via simple rules.

Discovery of a novel relation involving Littlewood-Richardson rule.

Asymmetric splitting of BPS indices based on degree difference.

Abstract

We introduce non-trivial two-point functions of the super Schur polynomials in the ABJM matrix model and study their exact values with the Fermi gas formalism. We find that, although defined non-trivially, these two-point functions enjoy two simple relations with the one-point functions. One of them is associated with the Littlewood-Richardson rule, while the other is more novel. With plenty of data, we also revisit the one-point functions and study how the diagonal BPS indices are split asymmetrically by the degree difference.