Ground State of Supermembrane on PP-wave

TL;DR

This paper investigates the ground state of supermembranes in a maximally supersymmetric pp-wave background, revealing a non-trivial structure and constructing explicit normalizable wave functions using quantum-mechanical methods.

Contribution

It provides the first explicit construction of the supersymmetric ground-state wave function for supermembranes on a pp-wave background, including zero-mode and nonzero-mode analyses.

Findings

Explicit normalizable ground-state wave function for zero-mode Hamiltonian

Construction of a non-normalizable-like solution with asymptotic series

Identification of non-trivial structure in supermembrane ground state

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.