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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
D.L. Jafferis, A. Lewkowycz, J. Maldacena and S.J. Suh, Relative entropy equals bulk relative entropy, JHEP 06 (2016) 004 [arXiv:1512.06431] [INSPIRE].
H. Casini, Relative entropy and the Bekenstein bound, Class. Quant. Grav. 25 (2008) 205021 [arXiv:0804.2182] [INSPIRE].
A.C. Wall, A Proof of the generalized second law for rapidly-evolving Rindler horizons, Phys. Rev. D 82 (2010) 124019 [arXiv:1007.1493] [INSPIRE].
A.C. Wall, A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices, Phys. Rev. D 85 (2012) 104049 [Erratum ibid. 87 (2013) 069904] [arXiv:1105.3445] [INSPIRE].
T. Pálmai, Excited state entanglement in one dimensional quantum critical systems: Extensivity and the role of microscopic details, Phys. Rev. B 90 (2014) 161404 [arXiv:1406.3182] [INSPIRE].
P. Caputa and A. Veliz-Osorio, Entanglement constant for conformal families, Phys. Rev. D 92 (2015) 065010 [arXiv:1507.00582] [INSPIRE].
L. Taddia, F. Ortolani and T. Pálmai, Renyi entanglement entropies of descendant states in critical systems with boundaries: conformal field theory and spin chains, J. Stat. Mech. 1609 (2016) 093104 [arXiv:1606.02667] [INSPIRE].
E.M. Brehm and M. Broccoli, Correlation functions and quantum measures of descendant states, JHEP 04 (2021) 227 [arXiv:2012.11255] [INSPIRE].
E. Witten, A Mini-Introduction To Information Theory, Riv. Nuovo Cim. 43 (2020) 187 [arXiv:1805.11965] [INSPIRE].
F.C. Alcaraz, M.I. Berganza and G. Sierra, Entanglement of low-energy excitations in Conformal Field Theory, Phys. Rev. Lett. 106 (2011) 201601 [arXiv:1101.2881] [INSPIRE].
M.I. Berganza, F.C. Alcaraz and G. Sierra, Entanglement of excited states in critical spin chians, J. Stat. Mech. 1201 (2012) P01016 [arXiv:1109.5673] [INSPIRE].
N. Lashkari, Relative Entropies in Conformal Field Theory, Phys. Rev. Lett. 113 (2014) 051602 [arXiv:1404.3216] [INSPIRE].
G. Sárosi and T. Ugajin, Relative entropy of excited states in two dimensional conformal field theories, JHEP 07 (2016) 114 [arXiv:1603.03057] [INSPIRE].
A. Belin, N. Iqbal and S.F. Lokhande, Bulk entanglement entropy in perturbative excited states, SciPost Phys. 5 (2018) 024 [arXiv:1805.08782] [INSPIRE].
P. Calabrese, F.H.L. Essler and A.M. Läuchli, Entanglement entropies of the quarter filled hubbard model, J. Stat. Mech. 2014 (2014) P09025.
P. Ruggiero and P. Calabrese, Relative Entanglement Entropies in 1 + 1-dimensional conformal field theories, JHEP 02 (2017) 039 [arXiv:1612.00659] [INSPIRE].
J. Bhattacharya, M. Nozaki, T. Takayanagi and T. Ugajin, Thermodynamical Property of Entanglement Entropy for Excited States, Phys. Rev. Lett. 110 (2013) 091602 [arXiv:1212.1164] [INSPIRE].
D.D. Blanco, H. Casini, L.-Y. Hung and R.C. Myers, Relative Entropy and Holography, JHEP 08 (2013) 060 [arXiv:1305.3182] [INSPIRE].
F.-L. Lin, H. Wang and J.-j. Zhang, Thermality and excited state Rényi entropy in two-dimensional CFT, JHEP 11 (2016) 116 [arXiv:1610.01362] [INSPIRE].
E. Perlmutter, Virasoro conformal blocks in closed form, JHEP 08 (2015) 088 [arXiv:1502.07742] [INSPIRE].
P. Calabrese, J. Cardy and E. Tonni, Entanglement entropy of two disjoint intervals in conformal field theory II, J. Stat. Mech. 1101 (2011) P01021 [arXiv:1011.5482] [INSPIRE].
C.T. Asplund, A. Bernamonti, F. Galli and T. Hartman, Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches, JHEP 02 (2015) 171 [arXiv:1410.1392] [INSPIRE].
A. Belin, N. Iqbal and J. Kruthoff, Bulk entanglement entropy for photons and gravitons in AdS3 , SciPost Phys. 8 (2020) 075 [arXiv:1912.00024] [INSPIRE].
A. Belin and S. Colin-Ellerin, Bootstrapping quantum extremal surfaces. Part I. The area operator, JHEP 11 (2021) 021 [arXiv:2107.07516] [INSPIRE].
M. Gaberdiel, A General transformation formula for conformal fields, Phys. Lett. B 325 (1994) 366 [hep-th/9401166] [INSPIRE].
S. Datta, J.R. David, M. Ferlaino and S.P. Kumar, Higher spin entanglement entropy from CFT, JHEP 06 (2014) 096 [arXiv:1402.0007] [INSPIRE].
S. Datta, J.R. David, M. Ferlaino and S.P. Kumar, Universal correction to higher spin entanglement entropy, Phys. Rev. D 90 (2014) 041903 [arXiv:1405.0015] [INSPIRE].
S. Datta, J.R. David and S.P. Kumar, Conformal perturbation theory and higher spin entanglement entropy on the torus, JHEP 04 (2015) 041 [arXiv:1412.3946] [INSPIRE].
B.G. Chowdhury, S. Datta and J.R. David, Rényi divergences from Euclidean quenches, JHEP 04 (2020) 094 [arXiv:1912.07210] [INSPIRE].
J. de Boer and J.I. Jottar, Thermodynamics of higher spin black holes in AdS3 , JHEP 01 (2014) 023 [arXiv:1302.0816] [INSPIRE].
M. Ammon, A. Castro and N. Iqbal, Wilson Lines and Entanglement Entropy in Higher Spin Gravity, JHEP 10 (2013) 110 [arXiv:1306.4338] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2108.00898
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Chowdhury, B.G., David, J.R. Entanglement in descendants. J. High Energ. Phys. 2022, 3 (2022). https://doi.org/10.1007/JHEP02(2022)003
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2022)003