Abstract
We use the quantum null energy condition in strongly coupled two-dimensional field theories (QNEC2) as diagnostic tool to study a variety of phase structures, including crossover, second and first order phase transitions. We find a universal QNEC2 constraint for first order phase transitions with kinked entanglement entropy and discuss in general the relation between the QNEC2-inequality and monotonicity of the Casini-Huerta c-function. We then focus on a specific example, the holographic dual of which is modelled by three-dimensional Einstein gravity plus a massive scalar field with one free parameter in the self-interaction potential. We study translation invariant stationary states dual to domain walls and black branes. Depending on the value of the free parameter we find crossover, second and first order phase transitions between such states, and the c-function either flows to zero or to a finite value in the infrared. We present evidence that evaluating QNEC2 for ground state solutions allows to predict the existence of phase transitions at finite temperature.
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].
D. Harlow, Jerusalem lectures on black holes and quantum information, Rev. Mod. Phys. 88 (2016) 015002 [arXiv:1409.1231] [INSPIRE].
P. Hayden, S. Nezami, X.-L. Qi, N. Thomas, M. Walter and Z. Yang, Holographic duality from random tensor networks, JHEP 11 (2016) 009 [arXiv:1601.01694] [INSPIRE].
M. Van Raamsdonk, Lectures on Gravity and Entanglement, in the proceedings of the Theoretical advanced study institute in elementary particle physics: new frontiers in fields and strings, June 1–26, Boulder U.S.A. (2015), arXiv:1609.00026 [INSPIRE].
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, The entropy of Hawking radiation, arXiv:2006.06872 [INSPIRE].
R. Bousso, Z. Fisher, S. Leichenauer and A.C. Wall, Quantum focusing conjecture, Phys. Rev. D 93 (2016) 064044 [arXiv:1506.02669] [INSPIRE].
R. Bousso, Z. Fisher, J. Koeller, S. Leichenauer and A.C. Wall, Proof of the quantum null energy condition, Phys. Rev. D 93 (2016) 024017 [arXiv:1509.02542] [INSPIRE].
T.A. Malik and R. Lopez-Mobilia, Proof of the quantum null energy condition for free fermionic field theories, Phys. Rev. D 101 (2020) 066028 [arXiv:1910.07594] [INSPIRE].
J. Koeller and S. Leichenauer, Holographic proof of the quantum null energy condition, Phys. Rev. D 94 (2016) 024026 [arXiv:1512.06109] [INSPIRE].
S. Balakrishnan, T. Faulkner, Z.U. Khandker and H. Wang, A general proof of the quantum null energy condition, JHEP 09 (2019) 020 [arXiv:1706.09432] [INSPIRE].
F. Ceyhan and T. Faulkner, Recovering the QNEC from the ANEC, Commun. Math. Phys. 377 (2020) 999 [arXiv:1812.04683] [INSPIRE].
D. Grumiller, P. Parekh and M. Riegler, Local quantum energy conditions in non-Lorentz-invariant quantum field theories, Phys. Rev. Lett. 123 (2019) 121602 [arXiv:1907.06650] [INSPIRE].
A.C. Wall, Testing the generalized second law in 1 + 1 dimensional conformal vacua: an argument for the causal horizon, Phys. Rev. D 85 (2012) 024015 [arXiv:1105.3520] [INSPIRE].
S.S. Gubser and A. Nellore, Mimicking the QCD equation of state with a dual black hole, Phys. Rev. D 78 (2008) 086007 [arXiv:0804.0434] [INSPIRE].
R.A. Janik, J. Jankowski and H. Soltanpanahi, Nonequilibrium dynamics and phase transitions in holographic models, Phys. Rev. Lett. 117 (2016) 091603 [arXiv:1512.06871] [INSPIRE].
M. Attems et al., Thermodynamics, transport and relaxation in non-conformal theories, JHEP 10 (2016) 155 [arXiv:1603.01254] [INSPIRE].
R.A. Janik, J. Jankowski and H. Soltanpanahi, Quasinormal modes and the phase structure of strongly coupled matter, JHEP 06 (2016) 047 [arXiv:1603.05950] [INSPIRE].
M. Attems, Y. Bea, J. Casalderrey-Solana, D. Mateos, M. Triana and M. Zilhao, Phase transitions, inhomogeneous horizons and second-order hydrodynamics, JHEP 06 (2017) 129 [arXiv:1703.02948] [INSPIRE].
R.A. Janik, J. Jankowski and H. Soltanpanahi, Real-time dynamics and phase separation in a holographic first order phase transition, Phys. Rev. Lett. 119 (2017) 261601 [arXiv:1704.05387] [INSPIRE].
J.D. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
M. Bañados, Three-dimensional quantum geometry and black holes, AIP Conf. Proc. 484 (1999) 147 [hep-th/9901148] [INSPIRE].
M.M. Roberts, Time evolution of entanglement entropy from a pulse, JHEP 12 (2012) 027 [arXiv:1204.1982] [INSPIRE].
M.M. Sheikh-Jabbari and H. Yavartanoo, Excitation entanglement entropy in two dimensional conformal field theories, Phys. Rev. D 94 (2016) 126006 [arXiv:1605.00341] [INSPIRE].
C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory, Nucl. Phys. B 424 (1994) 443 [hep-th/9403108] [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].
C. Ecker, D. Grumiller, W. van der Schee, M.M. Sheikh-Jabbari and P. Stanzer, Quantum null energy condition and its (non)saturation in 2d CFTs, SciPost Phys. 6 (2019) 036 [arXiv:1901.04499] [INSPIRE].
Z.U. Khandker, S. Kundu and D. Li, Bulk matter and the boundary quantum null energy condition, JHEP 08 (2018) 162 [arXiv:1803.03997] [INSPIRE].
M. Mezei and J. Virrueta, The quantum null energy condition and entanglement entropy in quenches, arXiv:1909.00919 [INSPIRE].
C. Ecker, D. Grumiller, W. van der Schee and P. Stanzer, Saturation of the quantum null energy condition in far-from-equilibrium systems, Phys. Rev. D 97 (2018) 126016 [arXiv:1710.09837] [INSPIRE].
R.C. Myers and A. Singh, Comments on holographic entanglement entropy and RG flows, JHEP 04 (2012) 122 [arXiv:1202.2068] [INSPIRE].
H. Liu and M. Mezei, A refinement of entanglement entropy and the number of degrees of freedom, JHEP 04 (2013) 162 [arXiv:1202.2070] [INSPIRE].
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, A c-theorem for the entanglement entropy, J. Phys. A 40 (2007) 7031 [cond-mat/0610375] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Positive energy in Anti-de Sitter backgrounds and gauged extended supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
P. Chomaz, M. Colonna and J. Randrup, Nuclear spinodal fragmentation, Phys. Rept. 389 (2004) 263 [INSPIRE].
Y. Bea et al., Crossing a large-N phase transition at finite volume, JHEP 02 (2021) 061 [arXiv:2007.06467] [INSPIRE].
V. Balasubramanian, B.D. Chowdhury, B. Czech and J. de Boer, Entwinement and the emergence of spacetime, JHEP 01 (2015) 048 [arXiv:1406.5859] [INSPIRE].
W. Fischler and S. Kundu, Strongly Coupled Gauge Theories: High and Low Temperature Behavior of Non-local Observables, JHEP 05 (2013) 098 [arXiv:1212.2643] [INSPIRE].
C. Ecker, Entanglement entropy from numerical holography, Ph.D. thesis, TU Wien, Wien, Austria (2018), arXiv:1809.05529 [INSPIRE].
M. Attems, Y. Bea, J. Casalderrey-Solana, D. Mateos and M. Zilhão, Dynamics of phase separation from holography, JHEP 01 (2020) 106 [arXiv:1905.12544] [INSPIRE].
I.R. Klebanov, D. Kutasov and A. Murugan, Entanglement as a probe of confinement, Nucl. Phys. B 796 (2008) 274 [arXiv:0709.2140] [INSPIRE].
E. Kiritsis, F. Nitti and L. Silva Pimenta, Exotic RG flows from holography, Fortsch. Phys. 65 (2017) 1600120 [arXiv:1611.05493] [INSPIRE].
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
C. Charmousis, B. Gouteraux, B.S. Kim, E. Kiritsis and R. Meyer, Effective holographic theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [INSPIRE].
B. Gouteraux and E. Kiritsis, Generalized holographic quantum criticality at finite density, JHEP 12 (2011) 036 [arXiv:1107.2116] [INSPIRE].
L. Huijse, S. Sachdev and B. Swingle, Hidden Fermi surfaces in compressible states of gauge-gravity duality, Phys. Rev. B 85 (2012) 035121 [arXiv:1112.0573] [INSPIRE].
T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [INSPIRE].
D. Grumiller, P. Parekh and M. Riegler, Local quantum energy conditions in non-Lorentz-invariant quantum field theories, Phys. Rev. Lett. 123 (2019) 121602 [arXiv:1907.06650] [INSPIRE].
M. Baggioli and D. Giataganas, Detecting topological quantum phase transitions via the c-function, Phys. Rev. D 103 (2021) 026009 [arXiv:2007.07273] [INSPIRE].
C.-S. Chu and D. Giataganas, c-theorem for anisotropic RG flows from holographic entanglement entropy, Phys. Rev. D 101 (2020) 046007 [arXiv:1906.09620] [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: 2007.10367
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
Ecker, C., Grumiller, D., Soltanpanahi, H. et al. QNEC2 in deformed holographic CFTs. J. High Energ. Phys. 2021, 213 (2021). https://doi.org/10.1007/JHEP03(2021)213
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2021)213