Costello, Witten and Yamazaki proposed a 4d Chern-Simons theory as a unified way to engineer integrable models. In the presence of 'Disorder' defects (for non-ultralocal 2d theories), this correspondence has been established only classically. As a first quantum check, I will derive the matching of 1-loop divergences between the 4d and 2d theories. My assumptions are general and seem to isolate sigma-models among the 2d theories. (Based on 2309.16753)