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Families of Hitchin systems and N=2 theories | | Aswin Balasubramanian
; Jacques Distler
; Ron Donagi
; | | Date: |
3 Aug 2020 | | Abstract: | Motivated by the connection to 4d $mathcal{N}=2$ 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
$overline{mathcal{M}}_{0,4}$, we compute this vector bundle explicitly.
Finally, we give a classification of the allowed pairs $(O,H)$ that can arise
for any given $N$. | | Source: | arXiv, 2008.01020 | | Services: | Forum | Review | PDF | Favorites | |
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