Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-08-19
JHEP 0309:066,2003
Physics
High Energy Physics
High Energy Physics - Theory
27 pages, latex
Scientific paper
10.1088/1126-6708/2003/09/066
We study four dimensional N=2 G_2 supersymmetric gauge theory on R^3\times 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 Seiberg-Witten 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 one-forms on the Seiberg-Witten curve. We will also find evidence that the low-energy dynamics of G_2 gauge theories can effectively be described in terms of an auxiliary hyperelliptic curve.
Alishahiha Mohsen
Boer Jan de
Mosaffa Amir Esmaeil
Wijnhout Jeroen
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