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Paper   IPM / Physic / 8571
School of Physics
  Title:   MT-AdS/CFT Correspondence
  Author(s):  M. Torabian
  Status:   Preprint
  Year:  2007
  Supported by:  IPM
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 plane-wave backgrounds in terms of a 3+1 dimensional U(N) gauge theory. Inspired by the idea of discrete light-cone 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 light-cone 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 non-BPS D0-branes in the light-cone gauge on the plane-wave 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 plane-wave backgrounds and study its correspondence with supersymmetric conformal gauge theory

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