Large N Spectrum of two Matrices in a Harmonic Potential and BMN energies

TL;DR

This paper analyzes the spectrum of a two-matrix quantum system in a harmonic potential, deriving exact eigenstates and energies, and incorporating interactions to match the BMN string theory spectrum.

Contribution

It provides a novel framework treating one matrix exactly and the other as an impurity, deriving the full spectrum including string tension corrections.

Findings

Exact eigenstates and energies for the free case.

Inclusion of interactions yields the BMN spectrum.

Spectrum matches string theory predictions with corrections.

Abstract

The large N spectrum of the quantum mechanical hamiltonian of two hermitean matrices in a harmonic potential is studied in a framework where one of the matrices is treated exactly and the other is treated as a creation operator impurity in the background of the first matrix. For the free case, the complete set of invariant eigenstates and corresponding energies are obtained. When g_{YM}^2 interactions are added, it is shown that the full string tension corrected spectrum of BMN loops is obtained.