Extended Seiberg-Witten Theory and Integrable Hierarchy
Dec, 2006
49 pages
Published in:
- JHEP 01 (2007) 104
e-Print:
- hep-th/0612019 [hep-th]
Report number:
- FIAN-TD-10-06
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Abstract:
The prepotential of the effective N=2 super-Yang-Mills theory perturbed in the ultraviolet by the descendents of the single-trace chiral operators is shown to be a particular tau-function of the quasiclassical Toda hierarchy. In the case of noncommutative U(1) theory (or U(N) theory with 2N-2 fundamental hypermultiplets at the appropriate locus of the moduli space of vacua) or a theory on a single fractional D3 brane at the ADE singularity the hierarchy is the dispersionless Toda chain. We present its explicit solutions. Our results generalize the limit shape analysis of Logan-Schepp and Vershik-Kerov, support the prior work hep-th/0302191 which established the equivalence of these N=2 theories with the topological A string on CP^1 and clarify the origin of the Eguchi-Yang matrix integral. In the higher rank case we find an appropriate variant of the quasiclassical tau-function, show how the Seiberg-Witten curve is deformed by Toda flows, and fix the contact term ambiguity.Note:
- 49 pages Report-no: FIAN/TD-10/06, ITEP-TH-57-05, IHES-P/06/43 Subj-class: High Energy Physics - Theory: Exactly Solvable and Integrable Systems: Mathematical Physics
- gauge field theory: Yang-Mills
- supersymmetry: 2
- Seiberg-Witten model
- prepotential
- membrane model: D-brane
- membrane model: p-brane
- p-brane: 3
- field theory: Toda
- differential equations: hierarchy
- integrability
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