On the resolution of categorical symmetries in (Non-) Unitary Rational CFTs

We explore several aspects of the categorical symmetry-resolved entanglement entropy (SREE) in two-dimensional Rational Conformal Field Theories (RCFTs) and express it directly in terms of the modular data of the theory. Motivated by the SymTFT construction of arXiv:2409.02806, we provide a general formula for SREE that applies to symmetric (weakly/strongly) and cloaking boundary conditions as well as for fusion rings with multiplicities. We check the formula against several explicit examples. Additionally, we study symmetry resolution for both categorical and invertible symmetries in (non-)diagonal RCFTs and comment on the subtleties that arise in these cases. Finally, we extend our analysis to diagonal non-unitary RCFTs, focusing on theories with generalized Haagerup-Izumi modular data, and find full agreement with the given formula.