Non-renormalisation of coupling constants from categorical symmetries in two dimensions

Abstract: We study the role of categorical symmetries in constraining the renormalisation of couplings in two-dimensional non-linear sigma models with Wess-Zumino term. A large class of these theories admit self-duality symmetries associated with discrete gauging and T-duality. They are generically non-conformal, but we argue that a particular coupling is protected from quantum corrections by the categorical symmetry. We give strong evidence for this claim by showing that the $\beta$-function for this coupling vanishes to 2-loop order if and only if this symmetry is present. Furthermore, in cases where the target space is a group manifold, the non-renormalisation result can be proven to hold non-perturbatively.