Families of Hitchin systems and N=2 theories

Abstract: Motivated by the connection to 4d N=2 theories, we study the global behavior of families of tamely-ramified $SL_N$ Hitchin integrable systems as the underlying curve varies over the Deligne-Mumford moduli space of stable pointed curves. In particular, we describe a flat degeneration of the Hitchin system to a nodal base curve and show that the behaviour of the integrable system at the node is partially encoded in a pair (O,H) where O is a nilpotent orbit and H is a simple Lie subgroup of FO, the flavour symmetry group associated to O. The family of Hitchin systems is nontrivially-fibered over the Deligne-Mumford moduli space. We prove a non-obvious result that the Hitchin bases fit together to form a vector bundle over the compactified moduli space. For the particular case of $M_{0,4}$, we compute this vector bundle explicitly. Finally, we give a classification of the allowed pairs (O,H) that can arise for any given N. (This is joint work with Aswin Balasubramanian and Jacques Distler)

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar