Noncommutative aspects of string theory

In this thesis we explore non-commutative aspects of string theory. The study is divided into three topics: (1) M-atrix theory, (2) AdS/CFT correspondence and (3) renormalization of non commutative field theories. A description of the work done on these topics follows:; (1) M-atrix theory. We address the issue of correspondence between classical supergravity and quantum super Yang-Mills (or Matrix theory) expressions for the long-distance, low-velocity interaction potentials between 0-branes and bound states of branes. The leading-order potentials are reproduced by the F4 terms in the 1-loop SYM effective action. Using self-consistency considerations, we determine a universal combination of F6 terms in the 2-loop SYM effective action that corresponds to the subleading terms in the supergravity potentials in many cases, including 0-brane scattering off 1/8 supersymmetric 4⊥1∥0 and 4⊥4⊥4∥0 bound states representing extremal D = 5 and D = 4 black holes. We give explicit descriptions of these configurations in terms of 1/4 supersymmetric SYM backgrounds on dual tori. Under a proper choice of the gauge field backgrounds, the 2-loop F6 SYM action reproduces the full expression for the subleading term in the supergravity potentials, including its subtle upsilon 2 part.; (2) AdS/CFT correspondence. We compute certain two-point functions in D = 4, N = 4, SU(N) SYM theory on the Coulomb branch using SUGRA/SYM duality and find an infinite set of first order poles at masses of order (Higgs scale)/( gY M N ).; (3) Renormalization of non-commutative field theories. A non-commutative Feynman graph is a ribbon graph and can be drawn on a genus g 2-surface with a boundary. We formulate a general convergence theorem for the non-commutative Feynman graphs in topological terms and give an outline of the proof of the theorem. We give a detailed classification of divergent graphs in some massive non-commutative field theories and demonstrate the renormalizability of some of these theories.