This series consists of talks in the area of Superstring Theory.
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.
We find that there is no supersymmetric flavor/CP problem, mu-problem, cosmological moduli/gravitino problem or dimension four/five proton decay problem in a class of supersymmetric theories with O(1) GeV gravitino mass. The cosmic abundance of the non-thermally produced gravitinos naturally explains the dark matter component of the universe.