Studies of Transport Coefficients in Charged AdS4 Black Holes on κ-Deformed Space

Document Type : Regular article

Authors

1 Instituto de Física, Universidade Federal do Rio de Janeiro, Brazil.

2 Instituto Federal de Educacao

3 Instituto de F\'isica, Universidade Federal da Bahia-Campus Universit\'ario de Ondina

Abstract

In this work, we study the effect of κ-deformed space on the thermodynamic quantities, this is find through the holographic renormalization that provides the free energy, which is fundamental to deriving another thermodynamic quantities. For this scenario we consider a charged AdS4 black hole for an Einstein-Maxwell model where the derivative quadrivector is replaced by a deformed version inspired by Kaniadakis statistics. Besides, we extract the transport coefficient known as electrical conductivity.

Keywords

Main Subjects

 

Article PDF

[1] J. M. Maldacena, ”The Large N limit of superconformal field theories and supergravity”, Int. J. Theor. Phys. 38, 1113 (1999) [Adv. Theor. Math. Phys. 2, 231 (1998)], [hep-th/9711200].
[2] S. S. Gubser, I. R. Klebanov and A. M. Polyakov, ”Gauge theory correlators from noncritical string theory”, Phys. Lett. B 428, 105 (1998), [hep-th/9802109].
[3] E. Witten, ”Anti-de Sitter space and holography”, Adv. Theor. Math. Phys. 2, 253 (1998), [hep-th/9802150].
[4] O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz, ”Large N field theories, string theory and gravity”, Phys. Rept. 323, 183 (2000), [hep-th/9905111].
[5] S. Bhattacharyya, V. E. Hubeny, S. Minwalla and M. Rangamani, ”Nonlinear Fluid Dynamics from Gravity”, JHEP 0802, 045 (2008), [arXiv:0712.2456 [hep-th]].
[6] C. Eling and Y. Oz, ”Holographic Screens and Transport Coefficients in the Fluid/Gravity Correspondence”, Phys. Rev. Lett. 107, 201602 (2011), [arXiv:1107.2134 [hep-th]].
[7] M. Rangamani, ”Gravity and Hydrodynamics: Lectures on the fluid-gravity correspondence”, Class. Quant. Grav. 26, 224003 (2009), [arXiv:0905.4352 [hep-th]].
[8] G. Aarts, ”Two complex problems on the lattice: Transport coefficients and finite chemical potential”, Nucl. Phys. A 820, 57C (2009), [arXiv:0811.1850 [hep-ph]].
[9] W. J. Jiang, H. S. Liu, H. Lu and C. N. Pope, ”DC Conductivities with Momentum Dissipation in Horndeski Theories”, JHEP 1707, 084 (2017), [arXiv:1703.00922 [hep- th]].
[10] M. Baggioli and W. J. Li, ”Diffusivities bounds and chaos in holographic Horndeski theories”, JHEP 1707, 055 (2017), [arXiv:1705.01766 [hep-th]].
[11] Y. Z. Li and H. Lu, ”a-theorem for Horndeski gravity at the critical point”, Phys. Rev. D 97, no. 12, 126008 (2018), [arXiv:1803.08088 [hep-th]].
[12] H. S. Liu, ”Violation of Thermal Conductivity Bound in Horndeski Theory”, Phys. Rev. D 98, no. 6, 061902 (2018), [arXiv:1804.06502 [hep-th]].
[13] S. A. Hartnoll, ”Lectures on holographic methods for condensed matter physics”, Class. Quant. Grav. 26, 224002 (2009).
[14] S. Sachdev, ”What can gauge-gravity duality teach us about condensed matter physics?”, Ann. Rev. Condensed Matter Phys. 3, 9 (2012), [arXiv:1108.1197 [cond- mat.str-el]].
[15] P. Kovtun, D. T. Son and A. O. Starinets, ”Holography and hydrodynamics: Diffusion on stretched horizons”, JHEP 0310, 064 (2003), [hep-th/0309213].
[16] P. Kovtun, D. T. Son and A. O. Starinets, ”Viscosity in strongly interacting quantum field theories from black hole physics”, Phys. Rev. Lett. 94, 111601 (2005), [hep-th/0405231].
[17] X. H. Feng, H. S. Liu, H. L¨u and C. N. Pope, ”Black Hole Entropy and Viscosity Bound in Horndeski Gravity”, JHEP 1511, 176 (2015), [arXiv:1509.07142 [hep-th]].
[18] M. Sadeghi, ”Black Brane Solution in Rastall AdS Massive Gravity and Viscosity Bound”, Mod. Phys. Lett. A 33, no. 37, 1850220 (2018), [arXiv:1809.08698 [hep-th]].
[19] F. F. Santos, ”Rotating black hole with a probe string in Horndeski Gravity”, Eur. Phys. J. Plus 135, no. 10, 810 (2020), [arXiv:2005.10983 [hep-th]].
[20] M. Bravo-Gaete, F. F. Santos, ”Complexity of four-dimensional hairy Anti-de-Sitter black holes with a rotating string and shear viscosity in generalized scalar-tensor theories”, Eur.Phys.J.C 82 2, 101 (2022), arXiv:2010.10942 [hep-th].
[21] F. F. Santos, E. F. Capossoli and H. Boschi-Filho, ”AdS/BCFT correspondence and BTZ black hole thermodynamics within Horndeski gravity”, Phys. Rev. D 104, no.6, 066014 (2021), [arXiv:2105.03802 [hep-th]].
[22] L. Heisenberg, ”A systematic approach to generalisations of General Rel-ativity and their cosmological implications”, Phys. Rept. 796, 1 (2019) doi:10.1016/j.physrep.2018.11.006 [arXiv:1807.01725 [gr-qc]].
[23] B. G. da Costa, I. S. Gomez and M. Portesi, ”κ-Deformed quantum and classical mechanics for a system with position-dependent effective mass”, J. Math. Phys. 61, no.8, 082105 (2020), [arXiv:2007.11184 [quant-ph]].
[24] G. Kaniadakis, P. Quarati and A. M. Scarfone, ”Kinetical foundations of nonconventional statistics”, Physica 305 (2002), 76-83, [arXiv:cond-mat/0110066 [cond-mat.stat-mech]].
[25] G. Kaniadakis ”Non-linear kinetics underlying generalized statistics”, Physica A 296 (2001), 405-425, [arxiv:ocond-mat/0103467[cond-mat.stat-mech]].
[26] G. Kaniadakis and A. M. Scarfone, ”Quantum vortices in systems obeying a generalized exclusion principle”, Phys. Rev. A 64 (2001), 026106 doi:10.1103/PhysRevE.64.026106 [arXiv:cond-mat/0204230 [cond-mat]].
[27] A. Ballon-Bayona, H. Boschi-Filho, E. F. Capossoli and D. M. Rodrigues, ”Criticality from Einstein-Maxwell-dilaton holography at finite temperature and density”, Phys. Rev. D 102, no. 12, 126003 (2020), [arXiv:2006.08810 [hep-th]].
[28] X. Chen, L. Zhang, D. Li, D. Hou and M. Huang, ”Gluodynamics and deconfinement phase transition under rotation from holography”, arXiv:2010.14478 [hep-ph].
[29] A. Chamblin, R. Emparan, C. V. Johnson and R. C. Myers, ”Charged AdS black holes and catastrophic holography”, Phys. Rev. D 60, 064018 (1999) doi:10.1103/PhysRevD.60.064018 [hep-th/9902170].
[30] A. Chamblin, R. Emparan, C. V. Johnson and R. C. Myers, ”Holography, thermody-namics and fluctuations of charged AdS black holes”, Phys. Rev. D 60, 104026 (1999) [hep-th/9904197].
[31] S. A. Hartnoll and C. P. Herzog, ”Impure AdS/CFT correspondence”, Phys. Rev. D 77, 106009 (2008).
[32] A. Lucas, ”Conductivity of a strange metal: from holography to memory functions”, JHEP 1503, 071 (2015).
[33] M. Baggioli, ”Gravity, holography and applications to condensed matter”, arXiv:1610.02681 [hep-th].
[34] S. K. Chakrabarti, S. Chakrabortty and S. Jain, ”Proof of universality of electrical conductivity at finite chemical potential”, JHEP 1102, 073 (2011).
[35] S. A. Hartnoll and D. M. Hofman, ”Locally Critical Resistivities from Umklapp Scattering”, Phys. Rev. Lett. 108, 241601 (2012).
[36] G. Policastro, D. T. Son and A. O. Starinets, ”The Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma”, Phys. Rev. Lett. 87, 081601 (2001), [hep-th/0104066].
[37] G. Policastro, D. T. Son and A. O. Starinets, ”From AdS / CFT correspondence to hydrodynamics”, JHEP 0209, 043 (2002), [hep-th/0205052].
[38] N. Iqbal and H. Liu, ”Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm”, Phys. Rev. D 79, 025023 (2009), [arXiv:0809.3808 [hep-th]].
[39] S. Jain, ”Universal thermal and electrical conductivity from holography”, JHEP 1011, 092 (2010).
[40] D. W. Pang, ”Conductivity and Diffusion Constant in Lifshitz Backgrounds”, JHEP 1001, 120 (2010).
[41] S. Jain, R. Samanta and S. P. Trivedi, ”The Shear Viscosity in Anisotropic Phases”, JHEP 1510, 028 (2015).
[42] David Tong, ”Lectures on Holographic Conductivity”, Presented at Cracow School of Theoretical Physics, PP 1, (2013).
Volume 2, Issue 4
November 2022
Pages 45-54
  • Receive Date: 19 September 2022
  • Revise Date: 07 November 2022
  • Accept Date: 24 November 2022