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We argue for the matching of 1-loop divergences between 4d Chern-Simonstheory with Disorder defects and the corresponding integrable 2d sigma-modelsof non-ultralocal type. Starting from the 4d path integral, we show undergeneral assumptions that the 1-loop divergences localise to the 2d defects.They match the 'universal' formulae developed in [arXiv:2209.05502] for the1-loop RG flows of integrable 2d sigma-models. Our argument uses an alternatepath integral representation for the 1-loop effective action and the knownclassical equivalence between the 4d and 2d theories.

Equivalence of 1-loop RG flows in 4d Chern-Simons and integrable 2d sigma-models