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

We argue for the matching of 1-loop divergences between 4d Chern-Simons theory with Disorder defects and the corresponding integrable 2d σ-models of non-ultralocal type. Starting from the 4d path integral, we show under general assumptions that the 1-loop divergences localise to the 2d defects. They match the ‘universal’ formulae developed in [arXiv:2209.05502] for the 1-loop RG flows of integrable 2d σ-models. Our argument uses an alternate path integral representation for the 1-loop effective action and the known classical equivalence between the 4d and 2d theories.