Aspects of Noncommutativity and Holography in Field Theory and String Theory

TL;DR

This thesis explores noncommutative Yang-Mills theories and the AdS/CFT correspondence, analyzing perturbation expansions and holographic quantities in the BMN limit, revealing limitations and behaviors of these theories and geometries.

Contribution

It provides a partial summation approach for noncommutative Yang-Mills theories with arbitrary gauge groups and studies holographic quantities in the BMN limit of AdS/CFT.

Findings

No finite theta-summed Feynman rules for certain gauge groups.

Behavior of boundaries, geodesics, and propagators in the BMN limit.

Insights into the limitations of perturbation expansions in noncommutative theories.

Abstract

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.