Quantum Fields and Strings

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.

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 consider pure three dimensional quantum gravity with a negative cosmological constant. The torus partition function can be computed exactly as a sum over geometries, including all known quantum corrections. The answer provides important clues about the structure of quantum gravity; in particular, in order for the theory to be a proper quantum mechanical system some extra ingredients are needed beyond the usual real geometries considered in general relativity. One possiblity is that complex geometries need to be included; this leads to holomorphically factorized partition functions. These partition functions provide a wealth of information about black hole microphysics. For example, the Hawking-page phase transition can be studied exactly; it is a phase transition of the type described by Lee and Yang, which is associated with a condensation of zeros in the complex temperature plane.

I will present a construction of supersymmetric Wilson loop operators in N=4 SYM for an arbitrary path on an S3 subspace of space-time. I will show how they are evaluated in AdS and in particular that the string world-sheet is a generalized calibration with respect to an almost-complex structure associate to the supersymmetries preserved by the loop. I will present some special examples and in the case when the loop is restricted to an S2, some evidence that the calculation reduces to a perturbative calculation in YM in 2-dimensions on S2. This in turn is exactly soluble in terms of a 0-dimensional matrix model.