The Renormalization Group Equation in N=2 Supersymmetric Gauge Theories

TL;DR

This paper derives an exact renormalization group equation for the prepotential in N=2 supersymmetric SU(N_c) gauge theories with arbitrary flavors, extending previous results and verifying it up to 2-instanton order.

Contribution

It introduces a new differential equation for the prepotential that generalizes earlier SU(2) results to arbitrary N_c and N_f, with an explicit modular form for the beta function.

Findings

Derived the RG equation for the prepotential with mass dependence.

Explicit formula for the modular form when N_f=0.

Verified the equation up to 2-instanton order in weak coupling.

Abstract

We clarify the mass dependence of the effective prepotential in N=2 supersymmetric SU(N_c) gauge theories with an arbitrary number N_f<2N_c of flavors. The resulting differential equation for the prepotential extends the equations obtained previously for SU(2) and for zero masses. It can be viewed as an exact renormalization group equation for the prepotential, with the beta function given by a modular form. We derive an explicit formula for this modular form when N_f=0, and verify the equation to 2-instanton order in the weak-coupling regime for arbitrary N_f and N_c.