PIRSA:20120006 Scientific Series Mathematical physics

DOI10.48660/20120006

Series: Mathematical Physics

Koroteev, P. (2020). q-Opers, QQ-Systems, and Bethe Ansatz. Perimeter Institute. https://pirsa.org/20120006

Koroteev, Peter. q-Opers, QQ-Systems, and Bethe Ansatz. Perimeter Institute, Dec. 03, 2020, https://pirsa.org/20120006 

@misc{ pirsa_PIRSA:20120006,
  doi = {10.48660/20120006},
  url = {https://pirsa.org/20120006},
  author = {Koroteev, Peter},
  keywords = {Mathematical physics},
  language = {en},
  title = {q-Opers, QQ-Systems, and Bethe Ansatz},
  publisher = {Perimeter Institute},
  year = {2020},
  month = {dec},
  note = {PIRSA:20120006 see, \url{https://pirsa.org}}
}

Abstract

We introduce the notions of (G,q)-opers and Miura (G,q)-opers, where G is a simply-connected complex simple Lie group, and prove some general results about their structure. We then establish a one-to-one correspondence between the set of (G,q)-opers of a certain kind and the set of nondegenerate solutions of a system of XXZ Bethe Ansatz equations. This can be viewed as a generalization of the so-called quantum/classical duality which I studied with D. Gaiotto several years ago. q-Opers generalize classical side, while on the quantum side we have more general XXZ Bethe Ansatz equations. The generalization goes beyond the scope of physics of N=2 supersymmetric gauge theories.

 

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