Multi-instantons in large N Matrix Quantum Mechanics

TL;DR

This paper computes multi-instanton corrections to the ground state energy in large N Matrix Quantum Mechanics, linking them to quantum mechanics via the exact WKB method and verifying through large order behavior analysis.

Contribution

It introduces a non-perturbative difference equation to derive multi-instanton effects from quantum mechanics in large N matrix models.

Findings

Multi-instanton corrections match the large order behavior of the 1/N expansion.

The method applies to quartic potential and c=1 string models.

Results validate the connection between matrix models and quantum mechanics.

Abstract

We calculate the multi-instanton corrections to the ground state energy in large $N$ Matrix Quantum Mechanics. We find that they can be obtained, through a non-perturbative difference equation, from the multi-instanton series in conventional Quantum Mechanics, as determined by the exact WKB method. We test our results by verifying that the one-instanton correction controls the large order behavior of the $1/N$ expansion in the quartic potential and in the $c=1$ string.