On the Spectrum of PP-Wave Matrix Theory

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.

18 pages, 2 tables, v2: typos corrected and references added, v3: one reference added

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• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background
• Penrose limits and maximal supersymmetry
• Matrix Perturbation Theory For M-theory On a PP-Wave
• Homogeneous fluxes, branes and a maximally supersymmetric solution of M-theory
• Superspace Geometry for Supermembrane Backgrounds
• The M-Theory Two-Brane in AdS_4 x S^7 and AdS_7 x S^4

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• Free Energy and Phase Transition of the Matrix Model on a Plane-Wave
• Fuzzy Spheres in pp Wave Matrix String Theory
• Little String Theory from a Double-Scaled Matrix Model
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• Supersymmetry and Branes in M-theory Plane-waves
• Instantons of M(atrix) Theory in PP-Wave Background
• Two-Loop Partition Function in the Planar Plane-Wave Matrix Model
• Deformed Matrix Theories with N=8 and Fivebranes in the PP Wave Background
• Dynamical aspects of the plane-wave matrix model at finite temperature
• All Higher Genus BPS Membranes in the Plane Wave Background
• Extraction of parton distributions from lattice QCD
• The Dilatation Operator of $\mathcal{N}$ $=$ 4 SYM and Classical Limits of Spin Chains and Matrix Models
• Exact fuzzy sphere thermodynamics in matrix quantum mechanics
• The Supergravity Dual of the BMN Matrix Model
• One-Loop Flatness of Membrane Fuzzy Sphere Interaction in Plane-Wave Matrix Model
• Instantons, supersymmetric vacua, and emergent geometries
• 5D action for longitudinal five branes on a pp-wave
• Operator Mixing and the AdS/CFT correspondence
• Maximally Supersymmetric RG Flows in 4D and Integrability
• Spectrum of Eleven-dimensional Supergravity on a PP-wave Background
• Dynamical tachyons on fuzzy spheres
• 3D N=2 massive super Yang-Mills and membranes/D2-branes in a curved background
• Membrane Fuzzy Sphere Dynamics in Plane-Wave Matrix Model
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• Dirichlet Branes of the Covariant Open Supermembrane on a PP-wave Background
• Membranes from monopole operators in ABJM theory: large angular momentum and M-theoretic AdS_4/CFT_3
• Spherical transverse M5-branes from the plane wave matrix model
• Coarse-Graining the Lin-Maldacena Geometries
• Supersymmetric Intersections of M-branes and pp-waves
• Type IIA Supergravity Excitations in Plane-Wave Background
• Heterotic plane wave matrix models and giant gluons
• New BPS Configurations of BMN Matrix Theory
• Point-Like Graviton Scattering in Plane-Wave Matrix Model
• Matrix Reduction and the su(2|2) superalgebra in AdS/CFT
• Matrix models and non-Abelian T dual of $Ad{S}_5\times S^5$
• Witten index of BMN matrix quantum mechanics
• Nonperturbative test of the Maldacena-Milekhin conjecture for the BMN matrix model
• Emergence of longitudinal 7-branes and fuzzy S^4 in compactification scenarios of M(atrix) theory