# q-Opers, QQ-Systems, and Bethe Ansatz

### APA

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

### MLA

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

### BibTex

@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}} }

**Collection**

**Subject**

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.