Abstract
We continue our study of nonperturbative superpotentials of
four-dimensional 
= 2 supersymmetric gauge theories
with gauge group U(N) on 
3 × S1, broken to
= 1 due to a classical superpotential. In a
previous paper [1] we discussed how the low-energy
quantum superpotential can be obtained by substituting the Lax
matrix of the underlying integrable system directly into the
classical superpotential. In this paper we prove algebraically that
this recipe yields the correct factorization of the Seiberg-Witten
curves, which is an important check of the conjecture. We will also
give an independent proof using the algebraic-geometrical
interpretation of the underlying integrable system.
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