Matone's relation of N=2 super Yang-Mills and spectrum of Toda chain

TL;DR

This paper explores Matone's relation in N=2 super Yang-Mills theory, demonstrating its validity beyond localization methods and linking it to the spectrum of the Toda chain within the Nekrasov-Shatashvili framework.

Contribution

It provides a case study supporting Matone's relation without localization and discusses its implications for Toda chain spectra in the Nekrasov-Shatashvili scheme.

Findings

Magnetic expansion satisfies Matone's type relation

Relation holds beyond localization techniques

Implications for Toda chain spectrum in Nekrasov-Shatashvili scheme

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 < Tr\phi^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.