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Ground State of Supermembrane on PP-wave

Noriko Nakayama·Katsuyuki Sugiyama·Kentaroh Yoshida
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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.

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Noriko Nakayama, Katsuyuki Sugiyama, Kentaroh Yoshida. 2002-09-18. Ground State of Supermembrane on PP-wave. https://doi.org/10.1103/physrevd.68.026001

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