Extended SeibergWitten theory and integrable hierarchy
Abstract
The prepotential of the effective Script N = 2 superYangMills theory, perturbed in the ultraviolet by the descendents ∫d^{4}θ tr Φ^{k+1} of the singletrace chiral operators, is shown to be a particular taufunction of the quasiclassical Toda hierarchy. In the case of noncommutative U(1) theory (or U(N) theory with 2N2 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, and we present its explicit solution. Our results generalise the limit shape analysis of LoganSchepp and VershikKerov, support the prior work [1], which established the equivalence of these Script N = 2 theories with the topological A string on CP^{1}, and clarify the origin of the EguchiYang matrix integral. In the higher rank case we find an appropriate variant of the quasiclassical taufunction, show how the SeibergWitten curve is deformed by Toda flows, and fix the contact term ambiguity.
 Publication:

Journal of High Energy Physics
 Pub Date:
 January 2007
 DOI:
 10.1088/11266708/2007/01/104
 arXiv:
 arXiv:hepth/0612019
 Bibcode:
 2007JHEP...01..104M
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 49 pages