Factorization of Seiberg-Witten Curves and Compactification to Three Dimensions

Details Factorization of Seiberg-Witten Curves and Compactification to Three Dimensions Factorization of Seiberg-Witten Curves and Compactification to Three Dimensions

2003-05-21

arxiv.org/abs/hep-th/0305189v1

JHEP 0403 (2004) 010

Physics

High Energy Physics

High Energy Physics - Theory

laTeX, 14 pages, uses AMSmath

Scientific paper

10.1088/1126-6708/2004/03/010

We continue our study of nonperturbative superpotentials of four-dimensional N=2 supersymmetric gauge theories with gauge group U(N) on R^3 x S^1, broken to N=1 due to a classical superpotential. In a previous paper, hep-th/0304061, 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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