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Paper IPM / P / 8571  


Abstract:  
This thesis is devoted to study one of the most recent and
significant evolutions, maybe third revolution, of a theory formerly
known as string theory. This theoretical mutation is the observation
of duality between gravitational theories and gauge theories.
Through Maldacena conjecture, known as AdS/CFT correspondence there
is an equivalent description of quantum type IIB string theory on
asymptotically AdSxS or planewave backgrounds in terms of a 3+1
dimensional U(N) gauge theory. Inspired by the idea of discrete
lightcone quantization (DLCQ), in this thesis we present a
description for quantum dynamics of the very string theory. In fact
we propose a prescription to construct the DLCQ Hamiltonian for that
string theory in the sector with J units of lightcone momentum.
It is conjectured that the DLCQ Hamiltonian is exactly the
Hamiltonian of a 0+1 dimensional supersymmetric U(J) gauge theory,
or a Matrix Theory (MT) for short. This matrix theory is the theory
for the stabilized phase of a tachyonic system of J number nonBPS
D0branes in the lightcone gauge on the planewave background with
compact null direction. We give some pieces of evidence in support
of this proposal. Thus we propose a Matrix theory for quantum type
IIB string theory on AdS or planewave backgrounds and study its
correspondence with supersymmetric conformal gauge theory
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