On the notion of conductor in the local geometric Langlands correspondence

Under the local Langlands correspondence, the conductor of an irreducible representation of ${\text{Gl}}_n(F)$ is greater than the Swan conductor of the corresponding Galois representation. In this paper, we establish the geometric analogue of this statement by showing that the conductor of a categorical representation of the loop group is greater than the irregularity of the corresponding meromorphic connection.