N=2 Theories and Families of Hitchin Systems

Famously, the Coulomb branch geometry of a 4d N=2 theory is encoded in the data of a complex integrable system. In class-S, this is a Hitchin System. In the conformal case, we are naturally led to consider families of Hitchin systems over the (compactified) moduli space of punctured Riemann surfaces. This has several interesting new implications for mathematicians, but also at least one new on for physicists: the equivalence-class of the (nontrivial!) holomorphic vector bundle of Coulomb branches over the moduli space.

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