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Integrable line defects and 4d Chern-Simons theory

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I discuss an application of a recent construction of 2d integrable field theories from 4d Chern-Simons theory by Costello and Yamazaki. After a review of the construction, I consider integrable line defects in purely chiral models, such as the chiral WZW model and products/cosets thereof. Here, Wilson lines of the 4d Chern-Simons theory descend to line defects in 2d theories which break the conformal symmetry but preserve integrability, and the role of the spectral parameter is played by the complexified RG scale of line defects. Finally, I will mention the relation of our construction to thermodynamic Bethe ansatz and IM/ODE correspondence, which provide nonperturbative solutions for the dynamics of such defects. This talk is partially based on 1908.02289 and on an upcoming work of the speaker with K. Costello, D. Gaiotto, and J. Wu.