Geometric Phases in String Theory

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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.