Integrable systems and supersymmetric gauge theory
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...This structure was noticed in special cases [9-11] and deduced from the generalities of low energy supersymmetric effective field theory [12]....
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...ched by Witten in Section 2.3 of [2]. It has been observed that the Seiberg-Witten solutions of many N= 2 theories can be understood in terms of known complex integrable systems, as discussed e.g. in [38, 39, 40, 41]. Here we have constructed a large general class of theories for which the relevant complex integrable system is a Hitchin system. 19One ecient proof that the BPS equations are the Hitchin equations ...
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...ed to derive the dictionary for a large number of cases for the Coulomb branch. In fact, it is quite suggestive that in the description of N = 2 Yang-Mills theories with non-simply laced gauge groups [35], groups appear with a correspondence which is very similar to what we have found with the outer automorphisms (3.1) of Dynkin diagrams. In [35] this corresponds to exchanging the long and short roots...
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...ar X iv :h ep -t h/ 95 Dedicated to the memory of Claude Itzykson, recalling his gift for combining elegant physics and beautiful mathematics...
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"Integrable systems and supersymmetr..." refers background in this paper
...Each affine Dynkin diagram [8] defines a periodic Toda lattice [9, 10] via Lax operators...
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...The fact that the twisted Kac-Moody algebra respects a grading under the ‘dual’ Coxeter element [8] guarantees that the ‘instanton’ terms involving μ will have grade [μ] = 2h∨g ....
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