Abstract
With the aim to reveal universal features of hadronic matter and correlated Dirac insulators in strong AC-electric fields, we study the \( \mathcal{N}=2 \) supersymmetric QCD with a finite quark mass driven by a rotating electric field ℰ x + iℰ y = ℰeiΩt. The analysis is done in the holographically dual D3/D7 system in the co-rotating frame, effectively. The nonequilibrium phase diagram is determined from the threshold electric field at which the insulator phase breaks down to a conductive phase due to the AC version of the Schwinger mechanism. The external field induces a rotating current \( {\mathcal{J}}_x+\kern0.62em i{\mathcal{J}}_y=\mathcal{J}{e^i}^{\Omega t} \) originating from vacuum polarization and dissipative current in the insulating and conductive phases respectively. Intriguing features are observed as the frequency Ω approaches resonance with the meson excitation energy Ωmeson. There, the threshold minimizes and a condensate of vector mesons with oscillating current exists even in the zero driving field limit. This state, which we call Floquet condensate of vector mesons, is expected to be dynamically stable realizing a non-thermal fixed point that breaks time translational and reversal symmetries. Our finding has many similarities with exciton BEC discussed in solid state systems, where the semiconductor is to be replaced by materials hosting gapped Dirac electrons, e.g. 3D topological insulators or bismuth. Vector meson Floquet condensate may also have implications in the pre-thermalized dynamics in heavy ion collision experiments.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951) 664 [INSPIRE].
W. Heisenberg and H. Euler, Folgerungen aus der Diracschen Theorie des Positrons, Z. Phys. 1 (1936) 714.
V. Weisskopf, The electrodynamics of the vacuum based on the quantum theory of the electron, in Early quantum electrodynamics, A.I. Miller ed., Cambridge University Press, Cambridge U.K. (1995).
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
K. Hashimoto, S. Kinoshita, K. Murata and T. Oka, Holographic floquet states I: a strongly coupled Weyl semimetal, JHEP 05 (2017) 127 [arXiv:1611.03702] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
M. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Meson spectroscopy in AdS/CFT with flavor, JHEP 07 (2003) 049 [hep-th/0304032] [INSPIRE].
A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].
T. Albash, V.G. Filev, C.V. Johnson and A. Kundu, Quarks in an external electric field in finite temperature large N gauge theory, JHEP 08 (2008) 092 [arXiv:0709.1554] [INSPIRE].
J. Erdmenger, R. Meyer and J.P. Shock, AdS/CFT with flavour in electric and magnetic Kalb-Ramond fields, JHEP 12 (2007) 091 [arXiv:0709.1551] [INSPIRE].
S. Nakamura, Negative differential resistivity from holography, Prog. Theor. Phys. 124 (2010) 1105 [arXiv:1006.4105] [INSPIRE].
S. Nakamura, Nonequilibrium phase transitions and nonequilibrium critical point from AdS/CFT, Phys. Rev. Lett. 109 (2012) 120602 [arXiv:1204.1971] [INSPIRE].
T. Ishii and K. Murata, Floquet superconductor in holography, arXiv:1804.06785 [INSPIRE].
O. Bergman, G. Lifschytz and M. Lippert, Response of holographic QCD to electric and magnetic fields, JHEP 05 (2008) 007 [arXiv:0802.3720] [INSPIRE].
T. Albash, V.G. Filev, C.V. Johnson and A. Kundu, Finite temperature large N gauge theory with quarks in an external magnetic field, JHEP 07 (2008) 080 [arXiv:0709.1547] [INSPIRE].
S. Nakamura and H. Ooguri, Out of equilibrium temperature from holography, Phys. Rev. D 88 (2013) 126003 [arXiv:1309.4089] [INSPIRE].
K. Hashimoto, S. Kinoshita, K. Murata and T. Oka, Electric field quench in AdS/CFT, JHEP 09 (2014) 126 [arXiv:1407.0798] [INSPIRE].
H. Hoshino and S. Nakamura, Effective temperature of nonequilibrium dense matter in holography, Phys. Rev. D 91 (2015) 026009 [arXiv:1412.1319] [INSPIRE].
G.V. Dunne, Heisenberg-euler effective lagrangians: basics and extensions, hep-th/0406216.
F. Gelis and N. Tanji, Schwinger mechanism revisited, Prog. Part. Nucl. Phys. 87 (2016) 1.
A.S. Gorsky, K.A. Saraikin and K.G. Selivanov, Schwinger type processes via branes and their gravity duals, Nucl. Phys. B 628 (2002) 270 [hep-th/0110178] [INSPIRE].
G.W. Semenoff and K. Zarembo, Holographic Schwinger effect, Phys. Rev. Lett. 107 (2011) 171601 [arXiv:1109.2920] [INSPIRE].
J. Ambjørn and Y. Makeenko, Remarks on holographic Wilson loops and the Schwinger effect, Phys. Rev. D 85 (2012) 061901 [arXiv:1112.5606] [INSPIRE].
S. Bolognesi, F. Kiefer and E. Rabinovici, Comments on critical electric and magnetic fields from holography, JHEP 01 (2013) 174 [arXiv:1210.4170] [INSPIRE].
Y. Sato and K. Yoshida, Holographic description of the Schwinger effect in electric and magnetic fields, JHEP 04 (2013) 111 [arXiv:1303.0112] [INSPIRE].
Y. Sato and K. Yoshida, Potential Analysis in Holographic Schwinger Effect, JHEP 08 (2013) 002 [arXiv:1304.7917] [INSPIRE].
D.D. Dietrich, Worldline holographic Schwinger effect, Phys. Rev. D 90 (2014) 045024 [arXiv:1405.0487] [INSPIRE].
D. Kawai, Y. Sato and K. Yoshida, A holographic description of the Schwinger effect in a confining gauge theory, Int. J. Mod. Phys. A 30 (2015) 1530026 [arXiv:1504.00459] [INSPIRE].
K. Bitaghsir Fadafan and F. Saiedi, Holographic Schwinger effect in non-relativistic backgrounds, Eur. Phys. J. C 75 (2015) 612 [arXiv:1504.02432] [INSPIRE].
K. Hashimoto and T. Oka, Vacuum instability in electric fields via AdS/CFT: Euler-Heisenberg Lagrangian and Planckian thermalization, JHEP 10 (2013) 116 [arXiv:1307.7423] [INSPIRE].
K. Hashimoto, T. Oka and A. Sonoda, Electromagnetic instability in holographic QCD, JHEP 06 (2015) 001 [arXiv:1412.4254] [INSPIRE].
J. Sonner, Holographic Schwinger effect and the geometry of entanglement, Phys. Rev. Lett. 111 (2013) 211603 [arXiv:1307.6850] [INSPIRE].
W.-J. Li, Y. Tian and H.-b. Zhang, Periodically driven holographic superconductor, JHEP 07 (2013) 030 [arXiv:1305.1600] [INSPIRE].
M. Natsuume and T. Okamura, The enhanced holographic superconductor: is it possible?, JHEP 08 (2013) 139 [arXiv:1307.6875] [INSPIRE].
A. Biasi, P. Carracedo, J. Mas, D. Musso and A. Serantes, Floquet scalar dynamics in globa AdS, JHEP 04 (2018) 137 [arXiv:1712.07637] [INSPIRE].
C. Heinisch and M. Holthaus, Adiabatic preparation of Floquet condensates, J. Mod. Opt. 63 (2016) 1768.
Y. Murakami et al., Nonequilibrium steady states and transient dynamics of conventional superconductors under phonon driving, Phys. Rev. B 96 (2017) 045125.
M. Knap et al., Dynamical Cooper pairing in non-equilibrium electron-phonon systems, Phys. Rev. B 94 (2016) 214504.
M. Babadi et al., The theory of parametrically amplified electron-phonon superconductivity, Phys. Rev. B 96 (2017) 014512.
M.A. Sentef et al., Theory of laser-controlled competing superconducting and charge orders, Phys. Rev. Lett. 118 (2017) 087002.
F. Wilczek, Quantum time crystals, Phys. Rev. Lett. 109 (2012) 118901.
J. Berges, S. Borsányi and C. Wetterich, Prethermalization, Phys. Rev. Lett. 93 (2004) 142002 [hep-ph/0403234] [INSPIRE].
V. Khemani, A. Lazarides, R. Moessner and S.L. Sondhi, On the phase structure of driven quantum systems, Phys. Rev. Lett. 116 (2016) 250401.
D.V. Else, B. Bauer and C. Nayak, Floquet time crystals, arXiv:1603.08001.
J. Zhang et al., Observation of a discrete time crystal, arXiv:1609.08684.
S. Choi et al., Observation of discrete time-crystalline order in a disordered dipolar many-body system, arXiv:1610.08057.
K. Yoshioka, E. Chae and M. Kuwata-Gonokami, Transition to a Bose-Einstein condensate and relaxation explosion of excitons at sub-Kelvin temperatures, Nat. Commun. 2 (2011) 328.
Y. Fuseya, M. Ogata and H. Fukuyama, Transport properties and diamagnetism of Dirac electrons in bismuth, J. Phys. Soc. Jpn. 84 (2015) 012001.
Y. Murakami et al., Photo-induced enhancement of excitonic order, Phys. Rev. Lett. 119 (2017) 247601 [arXiv:1707.07706].
T. Nag et al., Dynamical synchronization transition in interacting electron systems, arXiv:1802.02161.
M.Z. Hasan and C.L. Kane, Topological insulators, Rev. Mod. Phys. 82 (2010) 3045 [arXiv:1002.3895] [INSPIRE].
X.L. Qi and S.C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83 (2011) 1057 [arXiv:1008.2026] [INSPIRE].
Y.H. Wang et al., Observation of Floquet-Bloch states on the surface of a topological insulator, Science 342 (2013) 453 [arXiv:1310.7563] [INSPIRE].
T. Suzuki and R. Shimano, Exciton Mott transition in Si revealed by TeraHertz spectroscopy, Phys. Rev. Lett. 109 (2012) 046402.
N.F. Mott, Metal-insulator transition, Rev. Mod. Phys. 40 (1968) 677 [INSPIRE].
R. Zimmermann, Many-particle theory of highly excited semiconductors, Teubner, Leipzig, Germany (1988).
L. He, Nambu-Jona-Lasinio model description of weakly interacting Bose condensate and BEC-BCS crossover in dense QCD-like theories, Phys. Rev. D 82 (2010) 096003 [arXiv:1007.1920] [INSPIRE].
D.E. Kharzeev, L.D. McLerran and H.J. Warringa, The effects of topological charge change in heavy ion collisions: ‘Event by event P and CP-violation’, Nucl. Phys. A 803 (2008) 227 [arXiv:0711.0950] [INSPIRE].
V. Skokov, A.Yu. Illarionov and V. Toneev, Estimate of the magnetic field strength in heavy-ion collisions, Int. J. Mod. Phys. A 24 (2009) 5925 [arXiv:0907.1396] [INSPIRE].
V. Voronyuk et al., (Electro-)magnetic field evolution in relativistic heavy-ion collisions, Phys. Rev. C 83 (2011) 054911 [arXiv:1103.4239] [INSPIRE].
A. Bzdak and V. Skokov, Event-by-event fluctuations of magnetic and electric fields in heavy ion collisions, Phys. Lett. B 710 (2012) 171 [arXiv:1111.1949] [INSPIRE].
W.-T. Deng and X.-G. Huang, Event-by-event generation of electromagnetic fields in heavy-ion collisions, Phys. Rev. C 85 (2012) 044907 [arXiv:1201.5108] [INSPIRE].
V.P. Frolov, Merger transitions in brane-black-hole systems: criticality, scaling and self-similarity, Phys. Rev. D 74 (2006) 044006 [gr-qc/0604114] [INSPIRE].
D. Mateos, R.C. Myers and R.M. Thomson, Holographic phase transitions with fundamental matter, Phys. Rev. Lett. 97 (2006) 091601 [hep-th/0605046] [INSPIRE].
D. Mateos, R.C. Myers and R.M. Thomson, Thermodynamics of the brane, JHEP 05 (2007) 067 [hep-th/0701132] [INSPIRE].
N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].
G.W. Gibbons and C.A.R. Herdeiro, Born-Infeld theory and stringy causality, Phys. Rev. D 63 (2001) 064006 [hep-th/0008052] [INSPIRE].
G.W. Gibbons, Pulse propagation in Born-Infeld theory: the world volume equivalence principle and the Hagedorn-like equation of state of the Chaplygin gas, Grav. Cosmol. 8 (2002) 2 [hep-th/0104015] [INSPIRE].
G. Gibbons, K. Hashimoto and P. Yi, Tachyon condensates, Carrollian contraction of Lorentz group and fundamental strings, JHEP 09 (2002) 061 [hep-th/0209034] [INSPIRE].
K.-Y. Kim, J.P. Shock and J. Tarrio, The open string membrane paradigm with external electromagnetic fields, JHEP 06 (2011) 017 [arXiv:1103.4581] [INSPIRE].
S. Coleman, More about the massive Schwinger model, Ann. Phys. 101 (1976) 239.
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: 1712.06786
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Kinoshita, S., Murata, K. & Oka, T. Holographic Floquet states II: Floquet condensation of vector mesons in nonequilibrium phase diagram. J. High Energ. Phys. 2018, 96 (2018). https://doi.org/10.1007/JHEP06(2018)096
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2018)096