Complex crystallographic reflection groups and Seiberg-Witten integrable systems: rank 1 case

2023/09/22 by Argyres, Philip C., Chalykh, Oleg, Lü, Yongchao · 1 citation
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2309.12760

Abstract

We consider generalisations of the elliptic Calogero--Moser systems associated to complex crystallographic groups in accordance to [1]. In our previous work [2], we proposed these systems as candidates for Seiberg--Witten integrable systems of certain SCFTs. Here we examine that proposal for complex crystallographic groups of rank one. Geometrically, this means considering elliptic curves T² with ℤ_m-symmetries, m=2,3,4,6, and Poisson deformations of the orbifolds (T²×ℂ)/ℤ_m. The m=2 case was studied in [2], while m=3,4,6 correspond to Seiberg--Witten integrable systems for the rank 1 Minahan--Nemeshansky SCFTs of type E_6,7,8. This allows us to describe the corresponding elliptic fibrations and the Seiberg--Witten differential in a compact elegant form. This approach also produces quantum spectral curves for these SCFTs, which are given by Fuchsian ODEs with special properties.

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