Quantum Mechanics, Random Matrices and BMN Gauge Theory

TL;DR

This paper reviews the connection between gauge theory operators, quantum mechanics, and random matrices in the context of the pp-wave/BMN correspondence, highlighting methods to determine string state properties and compute correlation functions.

Contribution

It introduces a simplified quantum mechanical Hamiltonian framework for analyzing gauge theory operators and explores the application of random matrices for evaluating correlation functions.

Findings

Eigenvalues and eigenvectors of the Hamiltonian determine string state properties.

Random matrices facilitate explicit calculations of correlation functions.

The approach simplifies the analysis of gauge/string duality in the BMN limit.

Abstract

We review how the identification of gauge theory operators representing string states in the pp-wave/BMN correspondence and their associated anomalous dimension reduces to the determination of the eigenvectors and the eigenvalues of a simple quantum mechanical Hamiltonian and analyze the properties of this Hamiltonian. Furthermore, we discuss the role of random matrices as a tool for performing explicit evaluation of correlation functions.