Citations per year

20092010201120122013510
Abstract: (arXiv)
I discuss particular solutions of the integrable systems, starting from well-known dispersionless KdV and Toda hierarchies, which define in most straightforward way the generating functions for the Gromov-Witten classes in terms of the rational complex curve. On the ``mirror'' side these generating functions can be identified with the simplest prepotentials of complex manifolds, and I present few more exactly calculable examples of them. For the higher genus curves, corresponding in this context to the non Abelian gauge theories via the topological gauge/string duality, similar solutions are constructed using extended basis of Abelian differentials, generally with extra singularities at the branching points of the curve.
Note:
  • 24 pages, based on talks, given at Workshop on combinatorics of moduli spaces, Hurwitz numbers, and cluster algebras; Abel Symposium 2008; and Geometry and integrability in mathematical physics 08
  • supersymmetric gauge theory
  • topological string
  • integrable system
  • talk: Troms 2008
  • talk: Luminy 2008
  • gauge field theory: abelian
  • gauge field theory: nonabelian
  • duality: string
  • integrability
  • prepotential