Nonrenormalization of coupling constants from categorical symmetries in two dimensions

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Abstract
We study the role of categorical symmetries in constraining the renormalization of couplings in two-dimensional nonlinear sigma models with a Wess-Zumino term. A large class of these theories admits self-duality symmetries associated with discrete gauging and T-duality. They are generically nonconformal, 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 β -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 nonrenormalization result can be proven to hold nonperturbatively.
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  • Science and Technology Facilities Council (ST/X000575/1)
  • Imperial College London

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