On Nonabelian Theories and Abelian Differentials

  • A. MarshakovEmail author
Part of the Abel Symposia book series (ABEL, volume 5)


I discuss integrable systems and their solutions arising in the context of supersymmetric gauge theories and topological string models. For the simplest cases these are particular singular solutions to the dispersionless KdV and Toda systems, and they produce in most straightforward way the generating functions for the Gromov-Witten classes, including well-known intersection and Hurwitz numbers, in terms of the “mirror” target-space rational complex curve. In order to generalize them to the higher genus curves, corresponding in this context to nonabelian gauge theories via the topological gauge/string duality, one has to solve a similar problem, using the Abelian differentials, generally with extra singularities at the branching points.


Partition Function Topological String Supersymmetric Gauge Theory Toda Chain Nekrasov Partition Function 
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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Theory Department, P.N. Lebedev Physics InstituteRussia and Institute of Theoretical and Experimental PhysicsMoscowRussia

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