Generalized symmetry resolution of entanglement in conformal field theory for twisted and anyonic sectors
Arpit Das, Javier Molina-Vilaplana, Pablo Saura-Bastida
Abstract
A comprehensive symmetry resolution of the entanglement entropy in ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>1</a:mn> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:mrow> </a:math> )-d rational conformal field theories with categorical noninvertible symmetries is presented. This amounts to symmetry resolving the entanglement with respect to the generalized twisted and anyonic charged sectors of the theory. The anyonic sectors label the irreducible representations of a modular fusion category defining the symmetry and can be understood through the ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mn>2</c:mn> <c:mo>+</c:mo> <c:mn>1</c:mn> </c:mrow> </c:math> )-d symmetry topological field theory that encodes the symmetry features of the conformal field theory. Using this, we define the corresponding generalized boundary-dependent charged moments necessary for the symmetry resolution of the entanglement entropy and find that, contrary to the case of invertible symmetries, the entanglement equipartition between different charged sectors at the next-to-leading order in the ultraviolet cutoff, is broken. Published by the American Physical Society 2024