Classification of All 1/2 BPS Solutions of the Tiny Graviton Matrix Theory

The tiny graviton matrix theory [hep-th/0406214] is proposed to describe DLCQ of type IIB string theory on the maximally supersymmetric plane-wave or AdS_5xS^5 background. In this paper we provide further evidence in support of the tiny graviton conjecture by focusing on the zero energy, half BPS configurations of this matrix theory and classify all of them. These vacua are generically of the form of various three sphere giant gravitons. We clarify the connection between our solutions and the half BPS configuration in N=4 SYM theory and their gravity duals. Moreover, using our half BPS solutions, we show how the tiny graviton Matrix theory and the mass deformed D=3, N=8 superconformal field theories are related to each other.