On the Spectrum of PP-Wave Matrix Theory

TL;DR

This paper analyzes the spectrum of a matrix model of DLCQ M-theory in a pp-wave background, revealing discrete energy levels, supersymmetric multiplets, and protected states with no perturbative corrections.

Contribution

It introduces a detailed spectral analysis of the pp-wave matrix model, identifying protected multiplets and their energy properties, which was not previously understood.

Findings

Discrete spectrum with mass terms lifts flat directions

Existence of a unique zero-energy ground state

Identification of protected short multiplets with uncorrected energies

Abstract

We study the spectrum of the recently proposed matrix model of DLCQ M-theory in a parallel plane (pp)-wave background. In contrast to matrix theory in a flat background this model contains mass terms, which lift the flat directions of the potential and renders its spectrum discrete. The supersymmetry algebra of the model groups the energy eigenstates into supermultiplets, whose members differ by fixed amounts of energy in great similarity to the representation of supersymmetry in AdS spaces. There is a unique and exact zero-energy groundstate along with a multitude of long and short multiplets of excited states. For large masses the quantum mechanical model may be treated perturbatively and we study the leading order energy shifts of the first excited states up to level two. Most interestingly we uncover a protected short multiplet at level two, whose energies do not receive perturbative corrections. Moreover, we conjecture the existence of an infinite series of similar protected multiplets in the pp-wave matrix model.