THE RENORMALIZATION-GROUP EQUATION IN N=2 SUPERSYMMETRIC GAUGE-THEORIES

We clarify the mass dependence of the effective prepotential in N = 2 supersymmetric SU(N-c) gauge theories with an arbitrary number N-f < 2 N(c) of flavors, The resulting differential equation for the prepotent ial extends the equations obtained previously for SU(2) and for zero m asses, 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 ver ify the equation to 2-instanton order in the weak-coupling regime for arbitrary N-f and N-c. We also extend the renormalization group equati on to the case of other classical gauge groups. (C) 1997 Elsevier Scie nce B.V.