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ModMax electrodynamics and holographic magnetotransport

José Barrientos1,2,*, Nicolás Cáceres3,†, Felipe Diaz4,‡, and Ulises Hernandez-Vera5,§

  • *Contact author: jbarrientos@academicos.uta.cl
  • †Contact author: ntcaceres@puc.cl
  • ‡Contact author: fdiaz@itmp.msu.ru
  • §Contact author: uhernandez.vera@gmail.com
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Phys. Rev. D 112, 086018 – Published 28 October, 2025

DOI: https://doi.org/10.1103/d3tj-4nd8

Abstract

We study magnetotransport in a holographic model where ModMax nonlinear electrodynamics is coupled to Einstein anti–de Sitter gravity. To incorporate momentum relaxation, we introduce spatially linear free scalar fields that break translational symmetry, resulting in an anisotropic medium. Using linear response theory, we compute the DC conductivity matrix in the presence of an external magnetic field, expressing the conductivities in terms of horizon data. Our results demonstrate how the nonlinear ModMax parameter modifies charge transport, particularly influencing the Hall angle and Nernst signal. The nonlinear corrections introduce distinct deviations in both longitudinal and Hall conductivities while preserving the characteristic temperature scaling of strange metals, offering new insights into strongly coupled systems with nonlinear electromagnetic interactions. Notably, the Nernst signal reproduces that of high-Tc cuprate superconductors showing a superconducting dome and a normal phase, with the ModMax deformation parameter tuning critical and onset temperatures. In the strongly nonlinear regime, we find evidence of an exotic state dominated by quasiparticle excitations in the dual material.

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References (161)

  1. G. ’t Hooft, Conf. Proc. C 930308, 284 (1993), arXiv:gr-qc/9310026.
  2. L. Susskind, J. Math. Phys. (N.Y.) 36, 6377 (1995).
  3. J. M. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998).
  4. E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998).
  5. S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B 428, 105 (1998).
  6. S. A. Hartnoll, Classical Quantum Gravity 26, 224002 (2009).
  7. J. Zaanen, Y.-W. Sun, Y. Liu, and K. Schalm, Holographic Duality in Condensed Matter Physics (Cambridge University Press, Cambridge, England, 2015).
  8. S. A. Hartnoll, A. Lucas, and S. Sachdev, arXiv:1612.07324.
  9. S. A. Hartnoll, C. P. Herzog, and G. T. Horowitz, Phys. Rev. Lett. 101, 031601 (2008).
  10. S. A. Hartnoll, C. P. Herzog, and G. T. Horowitz, J. High Energy Phys. 12 (2008) 015.
  11. G. T. Horowitz and M. M. Roberts, Phys. Rev. D 78, 126008 (2008).
  12. G. T. Horowitz, Lect. Notes Phys. 828, 313 (2011).
  13. R. B. Mann, Ann. Isr. Phys. Soc. 13, 311 (1997), arXiv:gr-qc/9709039.
  14. G. T. Horowitz and M. M. Roberts, J. High Energy Phys. 11 (2009) 015.
  15. E. Witten, Adv. Theor. Math. Phys. 2, 505 (1998).
  16. S. S. Gubser, Classical Quantum Gravity 22, 5121 (2005).
  17. S. S. Gubser, Phys. Rev. D 78, 065034 (2008).
  18. R. Gregory, S. Kanno, and J. Soda, J. High Energy Phys. 10 (2009) 010.
  19. H. B. Zeng and J.-P. Wu, Phys. Rev. D 90, 046001 (2014).
  20. Z. Zhou, J.-P. Wu, and Y. Ling, J. High Energy Phys. 08 (2015) 067.
  21. W.-J. Jiang, H.-S. Liu, H. Lu, and C. N. Pope, J. High Energy Phys. 07 (2017) 084.
  22. A. Cisterna and J. Oliva, Classical Quantum Gravity 35, 035012 (2018).
  23. A. Cisterna, S. Fuenzalida, M. Lagos, and J. Oliva, Eur. Phys. J. C 78, 982 (2018).
  24. A. Cisterna, C. Erices, X.-M. Kuang, and M. Rinaldi, Phys. Rev. D 97, 124052 (2018).
  25. A. Cisterna, L. Guajardo, and M. Hassaine, Eur. Phys. J. C 79, 418 (2019); 79, 710(E) (2019).
  26. M. M. Caldarelli, C. Charmousis, and M. Hassaïne, J. High Energy Phys. 10 (2013) 015.
  27. M. Baggioli, A. Cisterna, and K. Pallikaris, Phys. Rev. D 104, 104067 (2021).
  28. U. Hernandez-Vera, Phys. Rev. D 111, 084035 (2025).
  29. J.-W. Chen, Y.-J. Kao, and W.-Y. Wen, Phys. Rev. D 82, 026007 (2010).
  30. T. Faulkner, G. T. Horowitz, J. McGreevy, M. M. Roberts, and D. Vegh, J. High Energy Phys. 03 (2010) 121.
  31. T. Faulkner, N. Iqbal, H. Liu, J. McGreevy, and D. Vegh, arXiv:1003.1728.
  32. T. Faulkner and J. Polchinski, J. High Energy Phys. 06 (2011) 012.
  33. T. Faulkner, N. Iqbal, H. Liu, J. McGreevy, and D. Vegh, Phil. Trans. R. Soc. A 369, 1640 (2011).
  34. T. Faulkner, N. Iqbal, H. Liu, J. McGreevy, and D. Vegh, Phys. Rev. D 88, 045016 (2013).
  35. N. Grandi, V. Juričić, I. Salazar Landea, and R. Soto-Garrido, J. High Energy Phys. 05 (2021) 123.
  36. N. Grandi, V. Juričić, I. S. Landea, and R. Soto-Garrido, Phys. Rev. D 105, L081902 (2022).
  37. N. Grandi, V. Juričić, I. Salazar Landea, and R. Soto-Garrido, J. High Energy Phys. 01 (2024) 030.
  38. S. Bahamondes, I. Salazar Landea, and R. Soto-Garrido, J. High Energy Phys. 09 (2024) 080.
  39. C. Lopez-Arcos, H. Nastase, F. Rojas, and J. Murugan, J. High Energy Phys. 01 (2014) 036.
  40. T. Andrade, A. Krikun, K. Schalm, and J. Zaanen, Nat. Phys. 14, 1049 (2018).
  41. L. Alejo, P. Goulart, and H. Nastase, J. High Energy Phys. 09 (2019) 003.
  42. A. Donos and J. P. Gauntlett, J. High Energy Phys. 04 (2014) 040.
  43. T. Andrade and B. Withers, J. High Energy Phys. 05 (2014) 101.
  44. A. Donos and J. P. Gauntlett, J. High Energy Phys. 06 (2014) 007.
  45. M. Baggioli, K.-Y. Kim, L. Li, and W.-J. Li, Sci. China Phys. Mech. Astron. 64, 270001 (2021).
  46. D. P. Sorokin, Fortschr. Phys. 70, 2200092 (2022).
  47. M. Born and L. Infeld, Proc. R. Soc. A 144, 425 (1934).
  48. W. Heisenberg and H. Euler, Z. Phys. 98, 714 (1936).
  49. G. W. Gibbons and D. A. Rasheed, Nucl. Phys. B454, 185 (1995).
  50. E. S. Fradkin and A. A. Tseytlin, Phys. Lett. 163B, 123 (1985).
  51. O. Miskovic and R. Olea, Phys. Rev. D 83, 064017 (2011).
  52. O. Miskovic and R. Olea, Phys. Rev. D 83, 024011 (2011).
  53. A. Dey, P. Roy, and T. Sarkar, J. High Energy Phys. 04 (2018) 098.
  54. P. A. Cano, A. J. Murcia, A. Rivadulla Sánchez, and X. Zhang, J. High Energy Phys. 07 (2022) 010.
  55. G. Arenas-Henriquez, F. Diaz, and Y. Novoa, J. High Energy Phys. 05 (2023) 072.
  56. M. Bravo-Gaete, L. Guajardo, and J. Oliva, Phys. Rev. D 106, 024017 (2022).
  57. P. Bueno, P. A. Cano, J. Moreno, and G. van der Velde, Phys. Rev. D 107, 064050 (2023).
  58. A. Álvarez, M. Bravo-Gaete, M. M. Juárez-Aubry, and G. V. Rodríguez, Phys. Rev. D 105, 084032 (2022).
  59. F. F. Santos, M. Bravo-Gaete, M. M. Ferreira, and R. Casana, Fortschr. Phys. 72, 2400088 (2024).
  60. M. Bravo-Gaete, L. Guajardo, and F. F. Santos, Phys. Rev. D 107, 104032 (2023).
  61. F. F. Santos, M. Bravo-Gaete, O. Sokoliuk, and A. Baransky, Fortschr. Phys. 71, 2300008 (2023).
  62. F. Colipí-Marchant, C. Corral, D. Flores-Alfonso, and L. Sanhueza, Phys. Rev. D 107, 104042 (2023).
  63. M. Bravo-Gaete, F. F. Santos, J. A. Herrera-Mendoza, and D. F. Higuita-Borja, arXiv:2504.17081.
  64. S. Barbosa, S. Fichet, and L. de Souza, arXiv:2503.20910.
  65. H. H. Soleng, Phys. Rev. D 52, 6178 (1995).
  66. E. Ayon-Beato and A. Garcia, Phys. Rev. Lett. 80, 5056 (1998).
  67. H. A. Gonzalez, M. Hassaine, and C. Martinez, Phys. Rev. D 80, 104008 (2009).
  68. K. A. Bronnikov, Phys. Rev. D 63, 044005 (2001).
  69. E. Ayon-Beato and A. Garcia, Phys. Lett. B 493, 149 (2000).
  70. M. Cataldo, N. Cruz, S. del Campo, and A. Garcia, Phys. Lett. B 484, 154 (2000).
  71. M. Hassaine and C. Martinez, Phys. Rev. D 75, 027502 (2007).
  72. M. Hassaine and C. Martinez, Classical Quantum Gravity 25, 195023 (2008).
  73. H. Maeda, M. Hassaine, and C. Martinez, Phys. Rev. D 79, 044012 (2009).
  74. J. A. R. Cembranos, A. de la Cruz-Dombriz, and J. Jarillo, J. Cosmol. Astropart. Phys. 02 (2015) 042.
  75. J. Barrientos, P. A. González, and Y. Vásquez, Eur. Phys. J. C 76, 677 (2016).
  76. A. Cisterna, M. Hassaine, J. Oliva, and M. Rinaldi, Phys. Rev. D 94, 104039 (2016).
  77. B. Eslam Panah, Fortschr. Phys. 71, 2300012 (2023).
  78. J. Jing and S. Chen, Phys. Lett. B 686, 68 (2010).
  79. J. Jing, Q. Pan, and S. Chen, J. High Energy Phys. 11 (2011) 045.
  80. S. Gangopadhyay and D. Roychowdhury, J. High Energy Phys. 08 (2012) 104.
  81. Y. Liu, Y. Gong, and B. Wang, J. High Energy Phys. 02 (2016) 116.
  82. M. Baggioli and O. Pujolas, J. High Energy Phys. 12 (2016) 107.
  83. P. Wang, H. Wu, and H. Yang, Eur. Phys. J. C 79, 6 (2019).
  84. A. Chakraborty, Classical Quantum Gravity 37, 065021 (2020).
  85. Y.-S. An, T. Ji, and L. Li, J. High Energy Phys. 10 (2020) 023.
  86. C. Lai and Q. Pan, Nucl. Phys. B974, 115615 (2022).
  87. I. Bandos, K. Lechner, D. Sorokin, and P. K. Townsend, Phys. Rev. D 102, 121703 (2020).
  88. B. P. Kosyakov, Phys. Lett. B 810, 135840 (2020).
  89. I. Bandos, K. Lechner, D. Sorokin, and P. K. Townsend, J. High Energy Phys. 03 (2021) 022.
  90. H. Nastase, Phys. Rev. D 105, 105024 (2022).
  91. S. A. Hartnoll and C. P. Herzog, Phys. Rev. D 76, 106012 (2007).
  92. S. A. Hartnoll and P. Kovtun, Phys. Rev. D 76, 066001 (2007).
  93. M. Blake and A. Donos, Phys. Rev. Lett. 114, 021601 (2015).
  94. A. Amoretti and D. Musso, J. High Energy Phys. 09 (2015) 094.
  95. A. Amoretti, D. K. Brattan, N. Magnoli, and M. Scanavino, J. High Energy Phys. 08 (2020) 097.
  96. A. Amoretti, D. Arean, D. K. Brattan, and N. Magnoli, J. High Energy Phys. 05 (2021) 027.
  97. A. Amoretti, D. Arean, D. K. Brattan, and L. Martinoia, J. High Energy Phys. 11 (2021) 011.
  98. X.-H. Ge and Z. Xu, J. High Energy Phys. 03 (2024) 069.
  99. O. Domenech, M. Montull, A. Pomarol, A. Salvio, and P. J. Silva, J. High Energy Phys. 08 (2010) 033.
  100. M. Montull, O. Pujolas, A. Salvio, and P. J. Silva, Phys. Rev. Lett. 107, 181601 (2011).
  101. M. Montull, O. Pujolas, A. Salvio, and P. J. Silva, J. High Energy Phys. 04 (2012) 135.
  102. A. Salvio, J. High Energy Phys. 09 (2012) 134.
  103. A. Salvio, J. High Energy Phys. 03 (2013) 136.
  104. M. Natsuume and T. Okamura, Phys. Rev. D 106, 086005 (2022).
  105. S. A. Hartnoll, P. K. Kovtun, M. Muller, and S. Sachdev, Phys. Rev. B 76, 144502 (2007).
  106. K.-Y. Kim, K. K. Kim, Y. Seo, and S.-J. Sin, J. High Energy Phys. 07 (2015) 027.
  107. T. R. Chien, Z. Z. Wang, and N. P. Ong, Phys. Rev. Lett. 67, 2088 (1991).
  108. A. Tyler and A. Mackenzie, Physica (Amsterdam) 282–287C, 1185 (1997).
  109. E. Blauvelt, S. Cremonini, A. Hoover, L. Li, and S. Waskie, Phys. Rev. D 97, 061901 (2018).
  110. Y. Ahn, M. Baggioli, H.-S. Jeong, and K.-Y. Kim, Phys. Rev. B 108, 235104 (2023).
  111. Z. Xu, N. Ong, Y. Wang, T. Kakeshita, and S.-i. Uchida, Nature (London) 406, 486 (2000).
  112. Y. Wang, L. Li, M. Naughton, G. Gu, S. Uchida, and N. Ong, Phys. Rev. Lett. 95, 247002 (2005).
  113. L. Li, J. Checkelsky, S. Komiya, Y. Ando, and N. Ong, Nat. Phys. 3, 311 (2007).
  114. Y. Wang, L. Li, and N. Ong, Phys. Rev. B 73, 024510 (2006).
  115. V. Oganesyan and I. Ussishkin, Phys. Rev. B 70, 054503 (2004).
  116. G. Tartaglione, Master’s thesis, Padua University, 2022.
  117. H. Rathi and D. Roychowdhury, J. High Energy Phys. 07 (2023) 026.
  118. K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).
  119. D. Flores-Alfonso, B. A. González-Morales, R. Linares, and M. Maceda, Phys. Lett. B 812, 136011 (2021).
  120. Z. Amirabi and S. Habib Mazharimousavi, Eur. Phys. J. C 81, 207 (2021).
  121. J. Barrientos, A. Cisterna, M. Hassaine, and K. Pallikaris, Phys. Lett. B 860, 139214 (2025).
  122. S. de Haro, S. N. Solodukhin, and K. Skenderis, Commun. Math. Phys. 217, 595 (2001).
  123. P. Ferrero, J. P. Gauntlett, J. M. P. Ipiña, D. Martelli, and J. Sparks, Phys. Rev. D 104, 046007 (2021).
  124. R. C. Myers, Phys. Rev. D 60, 046002 (1999).
  125. A. Ashtekar and S. Das, Classical Quantum Gravity 17, L17 (2000).
  126. R. M. Wald, Phys. Rev. D 10, 1680 (1974).
  127. D. Kastor, S. Ray, and J. Traschen, Classical Quantum Gravity 26, 195011 (2009).
  128. M. M. Caldarelli, G. Cognola, and D. Klemm, Classical Quantum Gravity 17, 399 (2000).
  129. J. Barrientos, A. Cisterna, D. Kubiznak, and J. Oliva, Phys. Lett. B 834, 137447 (2022).
  130. A. Chamblin, R. Emparan, C. V. Johnson, and R. C. Myers, Phys. Rev. D 60, 064018 (1999).
  131. D. C. Johnston, Advances in Thermodynamics of the van der Waals Fluid (Morgan & Claypool Publishers, San Rafael, 2014).
  132. O. Ökcü and E. Ayd𝚤ner, Eur. Phys. J. C 77, 24 (2017).
  133. O. Ökcü and E. Ayd𝚤ner, Eur. Phys. J. C 78, 123 (2018).
  134. J.-X. Mo and G.-Q. Li, Classical Quantum Gravity 37, 045009 (2020).
  135. A. Cisterna, S.-Q. Hu, and X.-M. Kuang, Phys. Lett. B 797, 134883 (2019).
  136. J. Barrientos and J. Mena, Phys. Rev. D 106, 044064 (2022).
  137. F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw Hill, Tokyo, 1965).
  138. A. Donos and J. P. Gauntlett, J. High Energy Phys. 11 (2014) 081.
  139. E. Witten, arXiv:hep-th/0112258.
  140. I. Papadimitriou, J. High Energy Phys. 05 (2007) 075.
  141. A. Anabalon, D. Astefanesei, D. Choque, and C. Martinez, J. High Energy Phys. 03 (2016) 117.
  142. N. Caceres, C. Corral, F. Diaz, and R. Olea, J. High Energy Phys. 05 (2024) 125.
  143. H. Kontani, arXiv:cond-mat/0204193.
  144. J. Hernandez and P. Kovtun, J. High Energy Phys. 05 (2017) 001.
  145. A. Amoretti and D. K. Brattan, Mod. Phys. Lett. A 37, 2230010 (2022).
  146. K. Behnia, J. Phys. Condens. Matter 35, 074003 (2022).
  147. D. Flores-Alfonso, R. Linares, and M. Maceda, J. High Energy Phys. 09 (2021) 104.
  148. A. Ballon Bordo, D. Kubizňák, and T. R. Perche, Phys. Lett. B 817, 136312 (2021).
  149. E. Ayón-Beato, D. Flores-Alfonso, and M. Hassaine, Phys. Rev. D 110, 064027 (2024).
  150. P. Meert and H. Nastase, Phys. Rev. D 110, 046004 (2024).
  151. T. Hale, D. Kubizňák, J. Menšíková, R. B. Mann, and J. Yang, Phys. Rev. D 111, 104004 (2025).
  152. G. Arenas-Henriquez, R. Gregory, and A. Scoins, J. High Energy Phys. 05 (2022) 063.
  153. G. Arenas-Henriquez, A. Cisterna, F. Diaz, and R. Gregory, J. High Energy Phys. 09 (2023) 122.
  154. A. Cisterna, F. Diaz, R. B. Mann, and J. Oliva, J. High Energy Phys. 11 (2023) 073.
  155. J. Tian and T. Lai, arXiv:2312.13718.
  156. C. R. D. Bunney and R. B. Mann, Classical Quantum Gravity 42, 075001 (2025).
  157. G. Arenas-Henriquez, F. Diaz, and D. Rivera-Betancour, J. High Energy Phys. 02 (2025) 007.
  158. S. Luo, arXiv:2412.21013.
  159. Z. Li, Z. Li, and J. Tian, J. High Energy Phys. 05 (2025) 161.
  160. D. Roychowdhury, J. High Energy Phys. 01 (2025) 134.
  161. R. Bel, K. Behnia, Y. Nakajima, K. Izawa, Y. Matsuda, H. Shishido, R. Settai, and Y. Onuki, Phys. Rev. Lett. 92, 217002 (2004).

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Phys. Rev. D 112, 086018– Published 28 October, 2025
  • Received 21 June 2025
  • Accepted 26 September 2025
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