## 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}. We also extend the renormalization group equation to the case of other classical gauge groups.

Original language | English |
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Pages (from-to) | 89-104 |

Number of pages | 16 |

Journal | Nuclear Physics B |

Volume | 494 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 9 Jun 1997 |

Externally published | Yes |

## Keywords

- Effective prepotential
- Instantons
- Modular forms
- Renormalization group
- Seiberg-Witten theory
- β-function