On the Spectrum of PP-Wave Matrix Theory

TL;DR

The paper analyzes the spectrum of a massive pp-wave matrix model arising in DLCQ M-theory, showing that mass terms discretize the spectrum and modify the supersymmetry algebra to yield energy-separated supermultiplets. Using a μ≫1 perturbative framework, the authors compute leading 1/m^2 energy shifts, revealing a uniquely protected short multiplet at level two and providing evidence for an infinite series of protected states, akin to BPS-like sectors in AdS/CFT. They also establish that the ground state energy remains exactly zero and discuss the potential extension of protection to higher-level symmetric states, with implications for M-theory in pp-wave backgrounds and possible dual field theories. These results illuminate nontrivial exact aspects of the M-theory pp-wave sector and motivate further exploration of protected sectors and large-N limits.

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.