This series consists of talks in the area of Superstring Theory.
We consider the large N limit of a class of fourdimensional supersymmetric theories in conjunction with a limit in their parameter space towards singular points where extra baryonic states become light, which causes the low-energy description to break down. However, this can be cured by defining a large N double scaling limit where one approaches the singularity by keeping the mass M of these states fixed. This limit has several interesting features.
I will describe the emergence of geometric (Berry) phases in supersymmetric systems.
In theories with degenerate states, non-Abelian geometric phases can arise.
I show how supersymmetry helps to ensure the existence of this phenomenon by invoking the examples of systems with (2,2) and (4,4) supersymmetry. In the former, I show how instantons contribute crucially to the form of the non-Abelian phase.
We describe simple systems where stringy instantons induce dynamical supersymmetry breaking, without any non-Abelian gauge dynamics. In suitable cases, a dual description via geometric transitions allows one to recast the instanton-generated superpotential as a classical flux superpotential. These simple DSB systems may have applications in model building.