Summing Up All Genus Free Energy of ABJM Matrix Model

TL;DR

This paper analyzes the free energy of the ABJM matrix model at large 't Hooft coupling, summing all genus corrections except worldsheet instantons, revealing a simple Airy function form that tests AdS/CFT correspondence.

Contribution

It provides a complete summation of all genus free energy contributions in the ABJM matrix model, expressed through an Airy function, advancing understanding of quantum gravity effects in AdS/CFT.

Findings

All genus free energy sums to an Airy function form.

The result tests the AdS/CFT correspondence at quantum gravity level.

Excludes worldsheet instanton contributions from the sum.

Abstract

The localization technique allows us to compute the free energy of the U(N)_k x U(N)_{-k} Chern-Simons-matter theory dual to type IIA strings on AdS_4 x CP^3 from weak to strong 't Hooft coupling \lambda = N / k at finite N, as demonstrated by Drukker, Marino, and Putrov. In this note we study further the free energy at large 't Hooft coupling with the aim of testing AdS/CFT at the quantum gravity level and, in particular, sum up all the 1/N corrections, apart from the worldsheet instanton contributions. The all genus partition function takes a remarkably simple form -- the Airy function, Ai (k^{4/3} \lambda_r), with the renormalized 't Hooft coupling \lambda_r.