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 F O , 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 .

A Panorama Of Physical Mathematics c. 2022

“…Among these the half-supersymmetric codimension two defects are among the most important. Their basic classification has been investigated in, for examples, [134][135][136]. These defects have an interesting operator product structure whose "structure constants" are themselves four-dimensional quantum field theories [137].…”