On nonabelian theories and abelian differentials

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Abstract

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.

Original languageEnglish
Title of host publicationDifferential Equations
Subtitle of host publicationGeometry, Symmetries and Integrability - The Abel Symposium 2008, Proceedings of the 5th Abel Symposium
Pages257-274
Number of pages18
DOIs
Publication statusPublished - 2009
Externally publishedYes
Event5th Abel Symposium 2008 - Differential Equations: Geometry, Symmetries and Integrability - Tromso, Norway
Duration: 17 Jun 200822 Jun 2008

Publication series

NameDifferential Equations: Geometry, Symmetries and Integrability - The Abel Symposium 2008, Proceedings of the 5th Abel Symposium

Conference

Conference5th Abel Symposium 2008 - Differential Equations: Geometry, Symmetries and Integrability
Country/TerritoryNorway
CityTromso
Period17/06/0822/06/08

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