q-Opers, QQ-Systems, and Bethe Ansatz


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}}

Peter Koroteev University of California, Berkeley


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.