Matrix theory for the discrete light-cone quantization of type IIB string theory on the AdS and/or plane-wave background

Abstract

We propose a recipe to construct the discrete light-cone quantization (DLCQ) Hamiltonian of type IIB string theory on the anti-de Sitter (AdS) (and/or plane-wave) background. We consider a system of $J$ number of coincident unstable non-Bogomol'nyi-Prasad-Sommerfield (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 worldline $U(J)$ gauge theory. This configuration suffers from tachyonic instabilities. Having instabilities be cured through the process of open string tachyon condensation, by expanding the theory about true minima of the effective potential and furthermore taking the 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.