Abstract
In this paper, we first study mutual information of excited states in the small subsystem size limit in generic conformal field theory. We then discuss relative entropy of two disjoint subsystems in the same limit.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Casini and M. Huerta, A finite entanglement entropy and the c-theorem, Phys. Lett. B 600 (2004) 142 [hep-th/0405111] [INSPIRE].
H. Casini and M. Huerta, On the RG running of the entanglement entropy of a circle, Phys. Rev. D 85 (2012) 125016 [arXiv:1202.5650] [INSPIRE].
H. Casini, M. Huerta, R.C. Myers and A. Yale, Mutual information and the F-theorem, JHEP 10 (2015) 003 [arXiv:1506.06195] [INSPIRE].
H. Casini, I.S. Landea and G. Torroba, The g-theorem and quantum information theory, JHEP 10 (2016) 140 [arXiv:1607.00390] [INSPIRE].
H. Casini, E. Teste and G. Torroba, Relative entropy and the RG flow, JHEP 03 (2017) 089 [arXiv:1611.00016] [INSPIRE].
T. Faulkner, R.G. Leigh, O. Parrikar and H. Wang, Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition, JHEP 09 (2016) 038 [arXiv:1605.08072] [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 [arXiv:1105.3445] [INSPIRE].
R. Bousso, H. Casini, Z. Fisher and J. Maldacena, Proof of a Quantum Bousso Bound, Phys. Rev. D 90 (2014) 044002 [arXiv:1404.5635] [INSPIRE].
R. Bousso, H. Casini, Z. Fisher and J. Maldacena, Entropy on a null surface for interacting quantum field theories and the Bousso bound, Phys. Rev. D 91 (2015) 084030 [arXiv:1406.4545] [INSPIRE].
N. Lashkari, M.B. McDermott and M. Van Raamsdonk, Gravitational dynamics from entanglement ‘thermodynamics’, JHEP 04 (2014) 195 [arXiv:1308.3716] [INSPIRE].
T. Faulkner, M. Guica, T. Hartman, R.C. Myers and M. Van Raamsdonk, Gravitation from Entanglement in Holographic CFTs, JHEP 03 (2014) 051 [arXiv:1312.7856] [INSPIRE].
M. Nozaki, T. Numasawa, A. Prudenziati and T. Takayanagi, Dynamics of Entanglement Entropy from Einstein Equation, Phys. Rev. D 88 (2013) 026012 [arXiv:1304.7100] [INSPIRE].
J. Lin, M. Marcolli, H. Ooguri and B. Stoica, Locality of Gravitational Systems from Entanglement of Conformal Field Theories, Phys. Rev. Lett. 114 (2015) 221601 [arXiv:1412.1879] [INSPIRE].
N. Lashkari, C. Rabideau, P. Sabella-Garnier and M. Van Raamsdonk, Inviolable energy conditions from entanglement inequalities, JHEP 06 (2015) 067 [arXiv:1412.3514] [INSPIRE].
N. Lashkari and M. Van Raamsdonk, Canonical Energy is Quantum Fisher Information, JHEP 04 (2016) 153 [arXiv:1508.00897] [INSPIRE].
N. Lashkari, J. Lin, H. Ooguri, B. Stoica and M. Van Raamsdonk, Gravitational positive energy theorems from information inequalities, PTEP 2016 (2016) 12C109 [arXiv:1605.01075] [INSPIRE].
B. Ning and F.-L. Lin, Relative Entropy and Torsion Coupling, Phys. Rev. D 94 (2016) 126007 [arXiv:1607.00263] [INSPIRE].
M. Wolf, F. Verstraete, M. Hastings and I. Cirac, Area Laws in Quantum Systems: Mutual Information and Correlations, Phys. Rev. Lett. 100 (2008) 070502 [arXiv:0704.3906].
P. Calabrese, J. Cardy and E. Tonni, Entanglement entropy of two disjoint intervals in conformal field theory, J. Stat. Mech. 0911 (2009) P11001 [arXiv:0905.2069] [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].
J. Cardy, Some results on the mutual information of disjoint regions in higher dimensions, J. Phys. A 46 (2013) 285402 [arXiv:1304.7985] [INSPIRE].
C. Agón and T. Faulkner, Quantum Corrections to Holographic Mutual Information, JHEP 08 (2016) 118 [arXiv:1511.07462] [INSPIRE].
L.-Y. Hung, R.C. Myers and M. Smolkin, Twist operators in higher dimensions, JHEP 10 (2014) 178 [arXiv:1407.6429] [INSPIRE].
M. Headrick, Entanglement Renyi entropies in holographic theories, Phys. Rev. D 82 (2010) 126010 [arXiv:1006.0047] [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [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].
G. Sárosi and T. Ugajin, Relative entropy of excited states in conformal field theories of arbitrary dimensions, JHEP 02 (2017) 060 [arXiv:1611.02959] [INSPIRE].
N. Lashkari, Modular Hamiltonian for Excited States in Conformal Field Theory, Phys. Rev. Lett. 117 (2016) 041601 [arXiv:1508.03506] [INSPIRE].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1611.03163
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Ugajin, T. Mutual information of excited states and relative entropy of two disjoint subsystems in CFT. J. High Energ. Phys. 2017, 184 (2017). https://doi.org/10.1007/JHEP10(2017)184
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2017)184