Entanglement in descendants

Abstract

We study the single interval entanglement and relative entropies of conformal descendants in 2d CFT. Descendants contain non-trivial entanglement, though the entanglement entropy of the canonical primary in the free boson CFT contains no additional entanglement compared to the vacuum, we show that the entanglement entropy of the state created by its level one descendant is non-trivial and is identical to that of the $U(1)$ current in this theory. We determine the first sub-leading corrections to the short interval expansion of the entanglement entropy of descendants in a general CFT from their four point function on the n-sheeted plane. We show that these corrections are determined by multiplying squares of appropriate dressing factors to the corresponding corrections of the primary. Relative entropy between descendants of the same primary is proportional to the square of the difference of their dressing factors. We apply our results to a class of descendants of generalized free fields and descendants of the vacuum and show that their dressing factors are universal.

58 pages, 7 figures

References in corpus (14)

• Entanglement entropy of two disjoint intervals in conformal field theory II
• Thermodynamical Property of Entanglement Entropy for Excited States
• Relative entropy and the Bekenstein bound
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Entanglement of low-energy excitations in Conformal Field Theory
• Relative Entropies in Conformal Field Theory
• A proof of the generalized second law for rapidly-evolving Rindler horizons
• Excited state entanglement in one dimensional quantum critical systems: Extensivity and the role of microscopic details
• Relative Entanglement Entropies in 1+1-dimensional conformal field theories
• A universal correction to higher spin entanglement entropy
• Thermality and excited state Rényi entropy in two-dimensional CFT
• Conformal perturbation theory and higher spin entanglement entropy on the torus
• Entanglement Entropies of the quarter filled Hubbard model
• Bootstrapping Quantum Extremal Surfaces I: The Area Operator