Matrix Theory for the DLCQ of Type IIB String Theory on the AdS/Plane-wave

Abstract

We propose a recipe to construct the DLCQ Hamiltonian of type IIB string theory on the AdS (and/or plane-wave) background. We consider a system of J number of coincident unstable non-BPS D0-branes of IIB theory in the light-cone gauge and on the plane-wave background with a compact null direction, the dynamics of which is described by the world-line U(J) gauge theory. This configuration suffers from tachyonic instabilities. Having instabilities been cured through the process of open string tachyon condensation, by expanding the theory about true minima of the effective potential and furthermore taking low energy limit to decouple the heavy modes, we end up with a 0+1-dimensional supersymmetric U(J) gauge theory, a Matrix Theory. We conjecture that the Hamiltonian of this Matrix Theory is just the DLCQ Hamiltonian of type IIB string theory on the AdS or equivalently plane-wave background in a sector with J units of light-cone momentum. We present some pieces of evidence in support of the proposal.