The effective prepotential of N = 2 supersymmetric SU(N) gauge theories

Abstract

We determine the effective prepotential for N=2 supersymmetric SU(N c ) gauge theories with an arbitrary number of flavors N f < 2N c , from the exact solution constructed out of spectral curves. The prepotential is the same for the several models of spectral curves proposed in the literature. It has to all orders the logarithmic singularities of the one-loop perturbative corrections, thus confirming the non-renormalization theorems from supersymmetry. In particular, the renormalized order parameters and their duals have all the correct monodromy transformations prescribed at weak coupling. We evaluate explicitly the contributions of one-and two-instanton processes.2

Calculating the prepotential by localization on the moduli space of instantons

“…Extracting even the oneinstanton coefficient of the prepotential is a lengthy calculation undertaken in Refs. [34,40]. It is interesting that the Seiberg-Witten theory predictions precisely match the expression (5.1a) of the non-commutative theory.…”

“…So the contribution from this critical-point set is of the form 34) where the VEV-independent constants I 1,2 are given by the following integrals (in the linearized form (2.15))…”

Two antisymmetric hypermultiplets in N = 2SU(N) gauge theory: Seiberg-Witten curve and M-theory interpretation

“…It is clear from this Table, however, that the renormalized order parameters are the natural variables for this problem, as emphasized in refs. [3] and [12]- [15]. …”

“…In particular, for SU(N ), the one-instanton prepotential has the form [3,13,14] 8πi one hypermultiplet in the antisymmetric representation and N f hypermultiplets in the defining representation, it is given by [12,14] 8πi…”

“…In this case systematic methods are available for extracting the relevant physical information [3]- [6].…”