# Quantum Elliptic Calogero-Moser Systems from Gauge Origami

## TL;DR

This paper explores the deep connections between quantum elliptic Calogero-Moser systems and supersymmetric gauge theories, introducing characteristic polynomials via orbifolded instanton partition functions and extending to the elliptic double Calogero-Moser system through gauge origami.

## Contribution

It constructs characteristic polynomials for eCM and edCM systems using gauge theory techniques, revealing new links between integrable systems and gauge theory defects.

## Key findings

- Constructed characteristic polynomial for eCM system.
- Extended construction to the elliptic double Calogero-Moser system.
- Linked gauge theory defects to integrable system properties.

## Abstract

We systematically study the interesting relations between the quantum elliptic Calogero-Moser system (eCM) and its generalization, and their corresponding supersymmetric gauge theories. In particular, we construct the suitable characteristic polynomial for the eCM system by considering certain orbifolded instanton partition function of the corresponding gauge theory. This is equivalent to the introduction of certain co-dimension two defects. We next generalize our construction to the folded instanton partition function obtained through the so-called "gauge origami" construction and precisely obtain the corresponding characteristic polynomial for the doubled version, named the elliptic double Calogero-Moser (edCM) system.