Abstract

For any abelian variety X with an action of a finite complex reflection group W, Etingof, Felder,Ma and Veselov constructed a family of integrable systems on T*X. When X is a product of ncopies of an eliptic curve E and W=Sn, this reproduces the usual elliptic Calogero-Mosersystem. Recently, together with Philip Argyres (Cincinnati) and Yongchao L (KIAS), we proposedthat many of these integrable systems at the classical level can be interpreted as Seiberg-Wittenintegrable systems of certain supersymmetric quantum field theories. l will describe our progress inunderstanding this connection for the case X= E" where E is an eliptic curve with the symmetrygroup Zm (of order m = 2, 3, 4, 6), and W is the wreath product of Zm and Sn. l will mostly talkabout n =1 case, which is already rather interesting. Based on: arXiv 2309.12760.