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Paper IPM / P / 6972  


Abstract:  
We study four dimensional N=2 G_{2} supersymmetric gauge theory on R^{3}×S^{1} deformed by a tree level superpotential. We will show that the exact superpotential can be obtained by making use of the Lax matrix of the corresponding integrable model which is the periodic Toda lattice based on the dual of the affine G_{2} Lie algebra. At extrema of the superpotential the SeibergWitten curve typically factorizes, and we study the algebraic equations underlying this factorization. For U(N) theories the factorization was closely related to the geometrical engineering of such gauge theories and to matrix model descriptions, but here we will find that the geometrical interpretation is more mysterious. Along the way we give a method to compute the gauge theory resolvent and a suitable set of oneforms on the SeibergWitten curve. We will also find evidence that the lowenergy dynamics of G_{2} gauge theories can effectively be described in terms of an auxiliary hyperelliptic curve.
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