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Revisiting the symmetry-resolved entanglement for noninvertible symmetries in 1+1d conformal field theories

Jared Heymann* and Thomas Quella†

  • *Contact author: j.heymann@unimelb.edu.au
  • †Contact author: Thomas.Quella@unimelb.edu.au
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Phys. Rev. D 112, 025004 – Published 7 July, 2025

DOI: https://doi.org/10.1103/lr47-yv3j

Abstract

Recently, a framework for computing the symmetry-resolved entanglement entropy for noninvertible symmetries in 1+1d conformal field theories has been proposed by Saura-Bastida et al. [Phys. Rev. D 109, 105026 (2024)]. We revisit their theoretical setup, paying particular attention to possible contributions from the conformal boundary conditions imposed at the entangling surface—a potential subtlety that was not addressed in the original proposal. We find that the presence of boundaries modifies the construction of projectors onto irreducible sectors, compared to what can be expected from a pure bulk approach. This is a direct consequence of the fusion algebra of noninvertible symmetries being different in the presence or absence of boundaries on which defects can end. We apply our formalism to the case of the Fibonacci category symmetry in the three-state Potts and tricritical Ising model and the Rep(S3) fusion category symmetry in the SU(2)4 Wess-Zumino-Witten conformal field theory. We numerically corroborate our findings by simulating critical anyonic chains with these symmetries. Our predictions for the symmetry-resolved entanglement for noninvertible symmetries seem to disagree with the recent work by Saura-Bastida et al.

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Phys. Rev. D 112, 025004– Published 7 July, 2025
  • Received 24 September 2024
  • Accepted 15 June 2025
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