Ground state of the supermembrane on appwave

We consider the ground state of a supermembrane on the maximally supersymmetric pp-wave background by using the quantum-mechanical procedure of de Wit, Hoppe, and Nicolai. On the pp-wave background the ground state has a nontrivial structure even in the zero-mode Hamiltonian. The supergravity multiplet in flat space comes to split with a certain energy difference. We explicitly derive the supersymmetric ground-state wave function for the zero-mode Hamiltonian, which is obviously normalizable. Moreover, we discuss the nonzero-mode Hamiltonian and construct an example of the ground-state wave function with the truncation of variables, whose ${L}^{2}$ norm can be represented by an asymptotic series.