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Categorical-Symmetry Resolved Entanglement in CFT

P. Saura-Bastida, A. Das, G. Sierra, J. Molina-Vilaplana

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.

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.
Paper Structure (4 sections, 55 equations, 1 figure, 1 table)

This paper contains 4 sections, 55 equations, 1 figure, 1 table.

Table of Contents

  1. A brief review of rational CFTs and Topological Defect Lines
  2. Leading contribution for SREE for finite groups
  3. The Tricritical Ising Model
  4. Fibonacci Anyons

Figures (1)

  • Figure 1: The factorization $ab$ imposes disks $\varepsilon \ll 1$ with boundary conditions $a$, $b$ (upper panel). The resulting manifold is replicated and after tracing over $\mathcal{H}_{B,ba}$, a conformal transformation yields an annulus of width $W$ and circumference $2\pi n$