Ground State of Supermembrane on PP-wave

Abstract

We consider the ground state of supermembrane on the maximally supersymmetric pp-wave background by using the quantum-mechanical procedure of de Wit-Hoppe-Nicolai. In the pp-wave case the ground state has non-trivial structure even in the zero-mode Hamiltonian, which is identical with that of superparticles on the pp-wave and resembles supersymmetric harmonic oscillators. The supergravity multiplet in the flat case is splitting with a certain energy difference. We explicitly construct the unique supersymmetric ground-state wave function of the zero-mode Hamiltonian, which is obviously normalizable. Moreover, we discuss the nonzero-mode Hamiltonian and construct an example for the ground-state wave function with a truncation of the variables. This special solution seems non-normalizable but its L^2-norm can be represented by an asymptotic series.

27 pages, LaTeX, typos corrected

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Cited by in corpus (24)

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• All Higher Genus BPS Membranes in the Plane Wave Background
• Dynamical aspects of the plane-wave matrix model at finite temperature
• D-branes of Covariant AdS Superstrings
• Thermodynamics of Fuzzy Spheres in PP-wave Matrix Model
• One-Loop Flatness of Membrane Fuzzy Sphere Interaction in Plane-Wave Matrix Model
• Spectrum of Eleven-dimensional Supergravity on a PP-wave Background
• Membrane Fuzzy Sphere Dynamics in Plane-Wave Matrix Model
• Euler Top Dynamics of Nambu-Goto P-Branes
• Dirichlet Branes of the Covariant Open Supermembrane on a PP-wave Background
• Dirichlet Branes of the Covariant Open Supermembrane in AdS_4 x S^7 and AdS_7 x S^4
• Supergravity, Supermembrane and M(atrix) model on PP-Waves
• Partition Function and Open/Closed String Duality in Type IIA String Theory on a PP-wave
• M-theory on a Time-dependent Plane-wave
• Thermodynamic Behavior of Fuzzy Membranes in PP-Wave Matrix Model
• Open M-branes on AdS_{4/7} x S^{7/4} Revisited
• The ground state of the D=11 supermembrane and matrix models on compact regions
• AdS and pp-wave D-particle superalgebras
• Point-Like Graviton Scattering in Plane-Wave Matrix Model
• Smearing Effect in Plane-Wave Matrix Model
• A Quantum Mechanical Model of Spherical Supermembranes
• Graviton and Spherical Graviton Potentials in Plane-Wave Matrix Model - overview and perspective -
• Probing Smearing Effect by Point-Like Graviton in Plane-Wave Matrix Model
• Zero-mode Spectrum of Eleven-dimensional Theory on the Plane-wave Background