PREPOTENTIALS OF N=2 SUPERSYMMETRIC GAUGE THEORIES AND SOLITON EQUATIONS

Abstract

Using recently proposed soliton equations we derive a basic identity for the scaling violation of N=2 supersymmetric gauge theories Σ i a i ∂F/∂a i −2F=8πib 1 u. Here F is the prepotential, a i ’s are the expectation values of the scalar fields in the vector multiplet, u=1/2 Tr<ϕ 2 > and b 1 is the coefficient of the one-loop β-function. This equation holds in the Coulomb branch of all N=2 supersymmetric gauge theories coupled with massless matter.