Aspects of Noncommutativity and Holography in Field Theory and String Theory

This thesis addresses two topics: noncommutative Yang-Mills theories and the AdS/CFT correspondence. In the first part we study a partial summation of the theta-expanded perturbation theory. The latter allows one to define noncommutative Yang-Mills theories with arbitrary gauge groups G as a perturbation expansion in the noncommutativity parameter theta. We show that for G being a subgroup of U(N) that is not identical to U(M) with M<N, one does not find a finite set of theta-summed Feynman rules. In the second part we study quantities which are important for the realization of the holographic principle in the AdS/CFT correspondence: boundaries, geodesics and the propagators of scalar fields. They should play a role in the holographic setup in the BMN limit as well. We observe how these quantities behave in the limiting process from AdS_5 x S^5 to the 10-dimensional plane wave which is the spacetime in the BMN limit.

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