Non Abelian gauge theories, prepotentials and Abelian differentials
Oct, 200824 pages
Published in:
- Theor.Math.Phys. 159 (2009) 598-617,
- Teor.Mat.Fiz. 159 (2009) 220-242
Contribution to:
e-Print:
- 0810.1536 [hep-th]
Report number:
- FIAN-TD-26-08,
- ITEP-TH-44-08
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Citations per year
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
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