Categorical-Symmetry Resolved Entanglement in CFT
Abstract
We propose a symmetry resolution of entanglement for categorical non-invertible symmetries (CaT-SREE) in (1 + 1)-dimensional CFTs. The definition parallels that of group-like invertible symmetries, employing the concept of symmetric boundary states with respect to a categorical symmetry. Our examination extends to rational CFTs, where the behavior of CaT-SREE mirrors that of group-like invertible symmetries. We find that CaT-SREE can be defined if there is no obstruction to gauging the categorical symmetry, as happens in the case of group-like symmetries. We also provide instances of the breakdown of entanglement equipartition at the next-to-leading order in the cutoff expansion. Our findings shed light on how the interplay between conformal boundary conditions and categorical symmetries lead to specific patterns in the entanglement entropy.
Keywords
Cite
@article{arxiv.2402.06322,
title = {Categorical-Symmetry Resolved Entanglement in CFT},
author = {P. Saura-Bastida and A. Das and G. Sierra and J. Molina-Vilaplana},
journal= {arXiv preprint arXiv:2402.06322},
year = {2024}
}
Comments
6 pages + 3 pages appendix, 1 figure. v2: matches published version