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This article focuses on the theoretical foundations of quantum physics, specifically exploring categorical symmetries and entanglement entropy within rational conformal field theories (RCFTs). The research derives general formulas for analyzing topological defect lines in both unitary and non-unitary systems, contributing directly to the mathematical framework of quantum computing and condensed matter theory.
On the resolution of categorical symmetries in (Non-) Unitary Rational CFTs
arXiv:2511.16363v3 Announce Type: replace-cross Abstract: We explore several aspects of categorical symmetry-resolved entanglement entropy (SREE) directly within two-dimensional rational conformal field theory (RCFT) (without invoking any SymTFT construction arXiv:2409.02806). We derive a general formula applicable whenever the action of the relevant topological defect lines on the annulus Hilbert space is known. This framework accommodates weakly and strongly symmetric boundaries, cloaking states, and fusion rings with multiplicities. We verify the formula in a range of diagonal unitary and non-unitary examples, including theories with generalized Haagerup-Izumi modular data. Furthermore, we extend the analysis to non-diagonal RCFTs. The $\frac{1}{2}E_6$ example demonstrates that closed-channel modular data and NIM-rep multiplicities alone do not suffice to determine the defect action on the complete open-channel Hilbert space.
Abstract:We explore several aspects of categorical symmetry-resolved entanglement entropy (SREE) directly within two-dimensional rational conformal field theory (RCFT) (without invoking any SymTFT construction arXiv:2409.02806). We derive a general formula applicable whenever the action of the relevant topological defect lines on the annulus Hilbert space is known. This framework accommodates weakly and strongly symmetric boundaries, cloaking states, and fusion rings with multiplicities. We verify the formula in a range of diagonal unitary and non-unitary examples, including theories with generalized Haagerup-Izumi modular data. Furthermore, we extend the analysis to non-diagonal RCFTs. The $\frac{1}{2}E_6$ example demonstrates that closed-channel modular data and NIM-rep multiplicities alone do not suffice to determine the defect action on the complete open-channel Hilbert space.
High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph); Quantum Algebra (math.QA); Quantum Physics (quant-ph)
arXiv:2511.16363 [hep-th]
(or arXiv:2511.16363v3 [hep-th] for this version)
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