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Nonrenormalization of coupling constants from categorical symmetries in two dimensions

Guillermo Arias-Tamargo ^*, Chris Hull ^†, and Maxwell L. Velásquez Cotini Hutt ^‡

Abdus Salam Centre for Theoretical Physics, The Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom

^*Contact author: g.arias-tamargo@imperial.ac.uk
^†Contact author: c.hull@imperial.ac.uk
^‡Contact author: m.hutt22@imperial.ac.uk

Phys. Rev. D 113, L061701 – Published 6 March, 2026

DOI: https://doi.org/10.1103/h56x-zgg8

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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Phys. Rev. D 113, L061701– Published 6 March, 2026

Vol. 113, Iss. 6 — 15 March 2026

Received 22 November 2025
Accepted 19 February 2026

DOI: https://doi.org/10.1103/h56x-zgg8

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Nonrenormalization of coupling constants from categorical symmetries in two dimensions

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