Quantum Fields and Strings

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. For example, the conventional \\\'t Hooft limit leads to a free theory of colour singlet states where all interactions are suppressed by powers of 1/N. In this case, the large N Hilbert space splits into two decoupled sectors, and one of them keeps residual interactions whose strength in inversely proportional to the mass M. We argue that for a class of these models the dynamics of this sector is dual to a non-critical superstring background, which is exactly solvable.

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. The latter system applies to D0-D4 brane dynamics in string theory, leading to a surprising re-interpretation of the Berry phase in terms of gravitational precession of a probe brane. Towards the end will comment on some work in progress on the geometric phase in (8,8) SUSY systems.