Quantum Geometry of Refined Topological Strings

Details Quantum Geometry of Refined Topological Strings Quantum Geometry of Refined Topological Strings

2011-05-03

arxiv.org/abs/1105.0630v1

Physics

High Energy Physics

High Energy Physics - Theory

64 pages, 2 figures

Scientific paper

We consider branes in refined topological strings. We argue that their wave-functions satisfy a Schr\"odinger equation depending on multiple times and prove this in the case where the topological string has a dual matrix model description. Furthermore, in the limit where one of the equivariant rotations approaches zero, the brane partition function satisfies a time-independent Schroedinger equation. We use this observation, as well as the back reaction of the brane on the closed string geometry, to offer an explanation of the connection between integrable systems and N=2 gauge systems in four dimensions observed by Nekrasov and Shatashvili.

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