Baxter Q-operators and supersymmetric gauge theories

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This scientific project concerns the study of quantum integrable models and their relations to gauge theories. It is motivated by the growing necessity for a thorough and deep understanding of the integrable structures behind N=4 super Yang-Mills theory and N=6 super Chern-Simons theory which may ultimately allow for a non-perturbative formulation of these supersymmetric gauge theories. The proposal contains two major research themes which are interrelated but can be investigated in parallel. The goal of the first theme is to make Q-operator methods available for N=4 super Yang-Mills theory by combining the known Q-operator construction for non-compact spin chains and the celebrated Quantum Spectral Curve of the gauge theory. The goal of the second theme is to develop the Q-operator construction of spin chains for orthosymplectic Lie superalgebras using results which can be extracted from the Seiberg-Witten curve of the corresponding N=2 quiver gauge theories. In particular, such Q-operators appear in N=6 super Chern-Simons theory. We hope that this project will reveal the underlying integrable model of N=4 super Yang-Mills theory at finite coupling but also open the door to apply Q-operator techniques to N=6 super Chern-Simons theory. Apart from that, our studies shall bring us closer to a universal formulation of the Q-operator construction of spin chains for general Lie algebras.