QM Research Seminar: Real Analytic Langlands for the Cylinder

Speaker: Jonah Baerman (​University of Hamburg).

Integrable models are omnipresent in theoretical physics, and can often be related to the study of supersymmetric gauge theories, where they can provide unprecedented access to nonperturbative information. For example, the low-energy behavior of certain 4d N=2 supersymmetric gauge theories is known to be described by so-called Hitchin systems, associated to a choice of Riemann surface Σ. By gauge theory/conformal field theory arguments, such models are expected to admit a dual description in terms of certain differential operators on Σ. We demonstrate this correspondence for the case of the twice-punctured sphere (the Toda chain), and find a geometric description of its quantization conditions. This allows us to apply integrability techniques, such as TBA equations, to the study of these differential operators, and vice versa. Lastly, we interpret our results as a real variant of the Analytic Langlands Correspondence. Based on past and ongoing work with Alba Grassi, Giovanni Ravazzini, and Jörg Teschner.