BIMSA > BIMSA Integrable Systems Seminar Elliptic complex reflection groups and Seiberg–Witten integrable systems
Elliptic complex reflection groups and Seiberg–Witten integrable systems
Organizers
Nicolai Reshetikhin , Ivan Sechin , Andrey Tsiganov
Speaker
Oleg Chalykh
Time
Tuesday, April 16, 2024 5:20 PM - 6:20 PM
Venue
A6-101
Online
Zoom 873 9209 0711 (BIMSA)
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 $n$ copies of an elliptic curve $E$ and $W=S_n$, this reproduces the usual elliptic Calogero­­-Moser system. Recently, together with Philip Argyres (Cincinnati) and Yongchao Lü (KIAS), we proposed that many of these integrable systems at the classical level can be interpreted as Seiberg­­-Witten integrable systems of certain super­symmetric quantum field theories. I will describe our progress in understanding this connection for the case $X=E^n$ where $E$ is an elliptic curve with the symmetry group $Z_m$ (of order $m=2,3,4,6$), and $W$ is the wreath product of $Z_m$ and $S_n$. I will mostly talk about $n=1$ case, which is already rather interesting. Based on: arXiv 2309.12760.