  In this doctoral thesis we study zero-mode spectra of Matrix theory and
eleven-dimensional supergravity on the plane-wave background. This background
is obtained via the Penrose limit of AdS_4 x S^7 and AdS_7 x S^4. The
plane-wave background is a maximally supersymmetric spacetime supported by
non-vanishing constant four-form flux in eleven-dimensional spacetime. First,
we discuss the Matrix theory on the plane-wave background suggested by
Berenstein, Maldacena and Nastase. We construct the Hamiltonian, 32
supercharges and their commutation relations. We discuss a spectrum of one
specific supermultiplet which represents the center of mass degrees of freedom
of N D0-branes. This supermultiplet would also represent a superparticle of the
eleven-dimensional supergravity in the large-N limit. Second, we study the
linearized supergravity on the plane-wave background in eleven dimensions.
Fixing the bosonic and fermionic fields in the light-cone gauge, we obtain the
spectrum of physical modes. We obtain the fact that the energies of the states
in Matrix theory completely correspond to those of fields in supergravity.
Thus, we find that the Matrix theory on the plane-wave background contains the
zero-mode spectrum of the eleven-dimensional supergravity completely. Through
this result, we can argue the Matrix theory on the plane-wave as a candidate of
quantum extension of eleven-dimensional supergravity, or as a candidate which
describes M-theory.
