Abstract
We extend the holographic Schwinger-Keldysh prescription introduced in [1] to charged black branes, with a view towards studying Hawking radiation in these backgrounds. Equivalently we study the real time fluctuations of the dual CFT held at finite temperature and finite chemical potential. We check our prescription using charged Dirac probe fields. We solve the Dirac equation in a boundary derivative expansion extending the results in [2]. The Schwinger-Keldysh correlators derived using this prescription automatically satisfy the appropriate KMS relations with Fermi-Dirac factors.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Glorioso, M. Crossley and H. Liu, A prescription for holographic Schwinger-Keldysh contour in non-equilibrium systems, arXiv:1812.08785 [INSPIRE].
R. Loganayagam, K. Ray and A. Sivakumar, Fermionic open EFT from holography, arXiv:2011.07039 [INSPIRE].
B. Chakrabarty, J. Chakravarty, S. Chaudhuri, C. Jana, R. Loganayagam and A. Sivakumar, Nonlinear Langevin dynamics via holography, JHEP 01 (2020) 165 [arXiv:1906.07762] [INSPIRE].
C. Jana, R. Loganayagam and M. Rangamani, Open quantum systems and Schwinger-Keldysh holograms, JHEP 07 (2020) 242 [arXiv:2004.02888] [INSPIRE].
D. T. Son and A. O. Starinets, Minkowski space correlators in AdS/CFT correspondence: recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].
C. P. Herzog and D. T. Son, Schwinger-Keldysh propagators from AdS/CFT correspondence, JHEP 03 (2003) 046 [hep-th/0212072] [INSPIRE].
D. T. Son and D. Teaney, Thermal noise and stochastic strings in AdS/CFT, JHEP 07 (2009) 021 [arXiv:0901.2338] [INSPIRE].
K. Skenderis and B. C. van Rees, Real-time gauge/gravity duality, Phys. Rev. Lett. 101 (2008) 081601 [arXiv:0805.0150] [INSPIRE].
K. Skenderis and B. C. van Rees, Real-time gauge/gravity duality: prescription, renormalization and examples, JHEP 05 (2009) 085 [arXiv:0812.2909] [INSPIRE].
B. C. van Rees, Real-time gauge/gravity duality and ingoing boundary conditions, Nucl. Phys. B Proc. Suppl. 192-193 (2009) 193 [arXiv:0902.4010] [INSPIRE].
R. G. Leigh and N. Nguyen hoang, Real-time correlators and non-relativistic holography, JHEP 11 (2009) 010 [arXiv:0904.4270] [INSPIRE].
G. C. Giecold, Fermionic Schwinger-Keldysh propagators from AdS/CFT, JHEP 10 (2009) 057 [arXiv:0904.4869] [INSPIRE].
E. Barnes, D. Vaman and C. Wu, Holographic real-time non-relativistic correlators at zero and finite temperature, Phys. Rev. D 82 (2010) 125042 [arXiv:1007.1644] [INSPIRE].
E. Barnes, D. Vaman, C. Wu and P. Arnold, Real-time finite-temperature correlators from AdS/CFT, Phys. Rev. D 82 (2010) 025019 [arXiv:1004.1179] [INSPIRE].
M. Botta-Cantcheff, P. J. Martínez and G. A. Silva, Interacting fields in real-time AdS/CFT, JHEP 03 (2017) 148 [arXiv:1703.02384] [INSPIRE].
J. de Boer, M. P. Heller and N. Pinzani-Fokeeva, Holographic Schwinger-Keldysh effective field theories, JHEP 05 (2019) 188 [arXiv:1812.06093] [INSPIRE].
J. S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [INSPIRE].
L. V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [Sov. Phys. JETP 20 (1965) 1018] [INSPIRE].
K.-C. Chou, Z.-B. Su, B.-L. Hao and L. Yu, Equilibrium and nonequilibrium formalisms made unified, Phys. Rept. 118 (1985) 1 [INSPIRE].
A. Kamenev, Field theory of non-equilibrium systems, Cambridge University Press, Cambridge, U.K. (2011).
M. L. Bellac, Thermal field theory, Cambridge University Press, Cambridge, U.K. (2011).
J. Rammer, Quantum field theory of non-equilibrium states, Cambridge University Press, Cambridge, U.K. (2007).
N. P. Landsman and C. G. van Weert, Real and imaginary time field theory at finite temperature and density, Phys. Rept. 145 (1987) 141 [INSPIRE].
N. Iqbal, H. Liu and M. Mezei, Lectures on holographic non-Fermi liquids and quantum phase transitions, in Theoretical Advanced Study Institute in Elementary Particle Physics. String theory and its applications: from meV to the Planck scale, World Scientific, Singapore (2011), pg. 707 [arXiv:1110.3814] [INSPIRE].
S. A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
S. A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [INSPIRE].
C. P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
B. Doucot, C. Ecker, A. Mukhopadhyay and G. Policastro, Density response and collective modes of semiholographic non-Fermi liquids, Phys. Rev. D 96 (2017) 106011 [arXiv:1706.04975] [INSPIRE].
S.-S. Lee, Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2 + 1 dimensions, Phys. Rev. B 80 (2009) 165102 [arXiv:0905.4532] [INSPIRE].
D. F. Mross, J. McGreevy, H. Liu and T. Senthil, A controlled expansion for certain non-Fermi liquid metals, Phys. Rev. B 82 (2010) 045121 [arXiv:1003.0894] [INSPIRE].
S. A. Hartnoll, P. K. Kovtun, M. Muller and S. Sachdev, Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes, Phys. Rev. B 76 (2007) 144502 [arXiv:0706.3215] [INSPIRE].
J. Zaanen, Y. Liu, Y.-W. Sun and K. Schalm, Holographic duality in condensed matter physics, Cambridge University Press, Cambridge, U.K. (2015).
R. Kubo, Statistical mechanical theory of irreversible processes. 1. General theory and simple applications in magnetic and conduction problems, J. Phys. Soc. Jap. 12 (1957) 570 [INSPIRE].
P. C. Martin and J. S. Schwinger, Theory of many particle systems. 1, Phys. Rev. 115 (1959) 1342 [INSPIRE].
M. Rangamani, Gravity and hydrodynamics: lectures on the fluid-gravity correspondence, Class. Quant. Grav. 26 (2009) 224003 [arXiv:0905.4352] [INSPIRE].
V. E. Hubeny, S. Minwalla and M. Rangamani, The fluid/gravity correspondence, in Theoretical Advanced Study Institute in Elementary Particle Physics. String theory and its applications: from meV to the Planck scale, (2012), pg. 348 [arXiv:1107.5780] [INSPIRE].
N. Ceplak, K. Ramdial and D. Vegh, Fermionic pole-skipping in holography, JHEP 07 (2020) 203 [arXiv:1910.02975] [INSPIRE].
M. Henningson and K. Sfetsos, Spinors and the AdS/CFT correspondence, Phys. Lett. B 431 (1998) 63 [hep-th/9803251] [INSPIRE].
W. Mueck and K. S. Viswanathan, Conformal field theory correlators from classical field theory on anti-de Sitter space. 2. Vector and spinor fields, Phys. Rev. D 58 (1998) 106006 [hep-th/9805145] [INSPIRE].
M. Henneaux, Boundary terms in the AdS/CFT correspondence for spinor fields, in International meeting on mathematical methods in modern theoretical physics (ISPM 98), (1998), pg. 161 [hep-th/9902137] [INSPIRE].
N. Iqbal and H. Liu, Real-time response in AdS/CFT with application to spinors, Fortsch. Phys. 57 (2009) 367 [arXiv:0903.2596] [INSPIRE].
S. Chaudhuri, C. Chowdhury and R. Loganayagam, Spectral representation of thermal OTO correlators, JHEP 02 (2019) 018 [arXiv:1810.03118] [INSPIRE].
U. Moitra, S. K. Sake and S. P. Trivedi, Near-extremal fluid mechanics, JHEP 02 (2021) 021 [arXiv:2005.00016] [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: 2011.08173
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
Loganayagam, R., Ray, K., Sharma, S.K. et al. Holographic KMS relations at finite density. J. High Energ. Phys. 2021, 233 (2021). https://doi.org/10.1007/JHEP03(2021)233
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2021)233