Matone's relation of N=2 super Yang-Mills and spectrum of Toda chain
arXiv:1103.3851 · doi:10.1088/0253-6102/56/5/18
Abstract
In N=2 super Yang-Mills theory, the Matone's relation relates instanton corrections of the prepotential to instanton corrections of scalar field condensation < Trϕ^2 >. This relation has been proved to hold for Omega deformed theories too, using localization method. In this paper, we first give a case study supporting the relation, which does not rely on the localization technique. Especially, we show that the magnetic expansion also satisfies a relation of Matone's type. Then we discuss implication of the relation for the spectrum of periodic Toda chain, in the context of recently proposed Nekrasov-Shatashvili scheme.
17 pages; v2 minor changes, references added; v3 more material added in 2nd section, clarification in 4th section