Skip to main content
SpringerLink
Log in

Overview of external electromagnetism and rotation in lattice QCD

  • Review
  • Published:
The European Physical Journal A Aims and scope Submit manuscript

Abstract

This is an introductory review of lattice QCD with external fields. The study of external magnetic fields is one of the greatest achievements in modern lattice QCD. Large-scale simulations and detailed analyses have revealed intriguing properties of QCD in the magnetic fields. The study of external electric fields is more challenging because of a technical difficulty. We overview the successes and challenges of the lattice simulations with the electromagnetic fields. We also introduce a newly developing field, the lattice simulation of rotating QCD matters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: No new data were analyzed in this paper.]

References

  1. K.G. Wilson, Phys. Rev. D 10, 2445 (1974)

    Article  ADS  Google Scholar 

  2. M. Creutz, Phys. Rev. D 21, 2308 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  3. S. Aoki, Flavour Lattice Averaging Group. Eur. Phys. J. C 80, 113 (2020)

    Article  ADS  Google Scholar 

  4. C. Gattringer, C.B. Lang, Quantum chromodynamics on the lattice, Vol. 788 of Lect. Notes Phys. (Springer, New York, 2010)

  5. H.J. Rothe, Lattice gauge theories: An Introduction, Vol. 82 of World Scientific Lect. Notes Phys. (World Scientific, Singapore, 2012)

  6. V..A. Miransky, I..A. Shovkovy, Phys. Rept. 576, 1 (2015)

  7. M. Eto, Y. Hirono, M. Nitta, S. Yasui, PTEP 2014, 012D01 (2014). arXiv:1308.1535

  8. D..E. Kharzeev, J. Liao, S..A. Voloshin, G. Wang, Prog. Part. Nucl. Phys. 88, 1 (2016)

  9. M..H. Al-Hashimi, U..J. Wiese, Ann. Phys. 324, 343 (2009)

  10. G.S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S.D. Katz, A. Schafer, K.K. Szabo, JHEP 02, 044 (2012)

  11. Y. Hidaka, A. Yamamoto, Phys. Rev. D 87, 094502 (2013). arXiv:1209.0007

  12. E.V. Luschevskaya, O.V. Larina, Nucl. Phys. B 884, 1 (2014)

  13. E.V. Luschevskaya, O.E. Solovjeva, O.A. Kochetkov, O.V. Teryaev, Nucl. Phys. B 898, 627 (2015)

  14. E.V. Luschevskaya, O.E. Solovjeva, O.V. Teryaev, Phys. Lett. B 761, 393 (2016). arXiv:1511.09316

    Article  ADS  Google Scholar 

  15. G.S. Bali, B.B. Brandt, G. Endrodi, B. Glassle, Phys. Rev. D 97, 034505 (2018). arXiv:1707.05600

  16. R. Bignell, W. Kamleh, D. Leinweber, Phys. Lett. B 811, 135853 (2020). arXiv:2005.10453

  17. H.T. Ding, S.T. Li, A. Tomiya, X.D. Wang, Y. Zhang (2020). arXiv:2008.00493

  18. F.X. Lee, S. Moerschbacher, W. Wilcox, Phys. Rev. D 78, 094502 (2008). arXiv:0807.4150

  19. E.V. Luschevskaya, O.V. Teryaev, D.Y. Golubkov, O.V. Solovjeva, R.A. Ishkuvatov, JHEP 11, 186 (2018). arXiv:1811.02344

    Article  ADS  Google Scholar 

  20. T. Primer, W. Kamleh, D. Leinweber, M. Burkardt, Phys. Rev. D 89, 034508 (2014), arXiv:1307.1509

  21. S.R. Beane, E. Chang, S. Cohen, W. Detmold, H.W. Lin, K. Orginos, A. Parreno, M.J. Savage, B.C. Tiburzi, Phys. Rev. Lett. 113, 252001 (2014). arXiv:1409.3556

  22. E. Chang, W. Detmold, K. Orginos, A. Parreno, M.J. Savage, B.C. Tiburzi, S.R. Beane, Phys. Rev. D 92, 114502 (2015). arXiv:1506.05518

  23. G.S. Bali, B.B. Brandt, G. Endrodi, B. Glassle, Phys. Rev. Lett. 121, 072001 (2018). arXiv:1805.10971

  24. K. Hattori, A. Yamamoto, PTEP 2019, 043B04 (2019). arXiv:1901.10182

  25. C. Bonati, M. D’Elia, M. Mariti, M. Mesiti, F. Negro, F. Sanfilippo, Phys. Rev. D 89, 114502 (2014). arXiv:1403.6094

  26. C. Bonati, M. D’Elia, M. Mariti, M. Mesiti, F. Negro, A. Rucci, F. Sanfilippo, Phys. Rev. D 94, 094007 (2016). arXiv:1607.08160

  27. C. Bonati, M. D’Elia, M. Mariti, M. Mesiti, F. Negro, A. Rucci, F. Sanfilippo, Phys. Rev. D 95, 074515 (2017). arXiv:1703.00842

  28. C. Bonati, S. Calì, M. D’Elia, M. Mesiti, F. Negro, A. Rucci, F. Sanfilippo, Phys. Rev. D 98, 054501 (2018). arXiv:1807.01673

  29. M. D’Elia, E. Meggiolaro, M. Mesiti, F. Negro, Phys. Rev. D 93, 054017 (2016). arXiv:1510.07012

  30. J.O. Andersen, W.R. Naylor, A. Tranberg, Rev. Mod. Phys. 88, 025001 (2016). arXiv:1411.7176

  31. V.P. Gusynin, V.A. Miransky, I.A. Shovkovy, Phys. Lett. B 349, 477 (1995). arXiv:hep-ph/9412257

    Article  ADS  Google Scholar 

  32. M. D’Elia, S. Mukherjee, F. Sanfilippo, Phys. Rev. D 82, 051501 (2010). arXiv:1005.5365

  33. M. D’Elia, F. Negro, Phys. Rev. D 83, 114028 (2011). arXiv:1103.2080

  34. G.S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S.D. Katz, A. Schafer, Phys. Rev. D 86, 071502 (2012). arXiv:1206.4205

  35. G.S. Bali, F. Bruckmann, G. Endrodi, F. Gruber, A. Schaefer, JHEP 04, 130 (2013). arXiv:1303.1328

    Article  ADS  Google Scholar 

  36. F. Bruckmann, G. Endrodi, T.G. Kovacs, JHEP 04, 112 (2013). arXiv:1303.3972

    Article  ADS  Google Scholar 

  37. E.M. Ilgenfritz, M. Muller-Preussker, B. Petersson, A. Schreiber, Phys. Rev. D 89, 054512 (2014). arXiv:1310.7876

  38. V.G. Bornyakov, P.V. Buividovich, N. Cundy, O.A. Kochetkov, A. Schäfer, Phys. Rev. D 90, 034501 (2014). arXiv:1312.5628

  39. G.S. Bali, F. Bruckmann, G. Endrödi, S.D. Katz, A. Schäfer, JHEP 08, 177 (2014). arXiv:1406.0269

    Article  ADS  Google Scholar 

  40. P. Cea, L. Cosmai, JHEP 12, 058 (2015). arXiv:1509.01982

    ADS  Google Scholar 

  41. M. D’Elia, F. Manigrasso, F. Negro, F. Sanfilippo, Phys. Rev. D 98, 054509 (2018). arXiv:1808.07008

  42. G. Endrodi, M. Giordano, S.D. Katz, T.G. Kovács, F. Pittler, JHEP 07, 007 (2019). arXiv:1904.10296

    Article  ADS  Google Scholar 

  43. V.V. Braguta, M.N. Chernodub, A.Y. Kotov, A.V. Molochkov, A.A. Nikolaev, Phys. Rev. D 100, 114503 (2019). arXiv:1909.09547

  44. H.T. Ding, C. Schmidt, A. Tomiya, X.D. Wang, Phys. Rev. D 102, 054505 (2020). arXiv:2006.13422

  45. G. Endrodi, JHEP 07, 173 (2015). arXiv:1504.08280

    Article  ADS  Google Scholar 

  46. C. Bonati, M. D’Elia, M. Mariti, F. Negro, F. Sanfilippo, Phys. Rev. Lett. 111, 182001 (2013). arXiv:1307.8063

  47. L. Levkova, C. DeTar, Phys. Rev. Lett. 112, 012002 (2014). arXiv:1309.1142

  48. C. Bonati, M. D’Elia, M. Mariti, F. Negro, F. Sanfilippo, Phys. Rev. D 89, 054506 (2014). arXiv:1310.8656

  49. G.S. Bali, F. Bruckmann, G. Endrodi, A. Schafer, Phys. Rev. Lett. 112, 042301 (2014). arXiv:1311.2559

  50. G.S. Bali, G. Endrődi, S. Piemonte, JHEP 07, 183 (2020). arXiv:2004.08778

    Article  ADS  Google Scholar 

  51. D.E. Kharzeev, L.D. McLerran, H.J. Warringa, Nucl. Phys. A 803, 227 (2008). arXiv:0711.0950

    Article  ADS  Google Scholar 

  52. K. Fukushima, D.E. Kharzeev, H.J. Warringa, Phys. Rev. D 78, 074033 (2008). arXiv:0808.3382

  53. P.V. Buividovich, E.V. Luschevskaya, M.I. Polikarpov, M.N. Chernodub, JETP Lett. 90, 412 (2009)

    Article  ADS  Google Scholar 

  54. P.V. Buividovich, M.N. Chernodub, E.V. Luschevskaya, M.I. Polikarpov, Phys. Rev. D 80, 054503 (2009). arXiv: 0907.0494

  55. M. Abramczyk, T. Blum, G. Petropoulos, R. Zhou, PoS LAT2009, 181 (2009). arXiv:0911.1348

  56. G.S. Bali, F. Bruckmann, G. Endrödi, Z. Fodor, S.D. Katz, A. Schäfer, JHEP 04, 129 (2014). arXiv:1401.4141

    Article  ADS  Google Scholar 

  57. N. Astrakhantsev, V.V. Braguta, M. D’Elia, A.Y. Kotov, A.A. Nikolaev, F. Sanfilippo, Phys. Rev. D 102, 054516 (2020). arXiv:1910.08516

  58. P.V. Buividovich, M.N. Chernodub, D.E. Kharzeev, T. Kalaydzhyan, E.V. Luschevskaya, M.I. Polikarpov, Phys. Rev. Lett. 105, 132001 (2010). arXiv:1003.2180

  59. A. Yamamoto, Phys. Rev. Lett. 107, 031601 (2011). arXiv:1105.0385

  60. A. Yamamoto, Phys. Rev. D 84, 114504 (2011). arXiv:1111.4681

  61. M. Puhr, P.V. Buividovich, Phys. Rev. Lett. 118, 192003 (2017). arXiv:1611.07263

  62. P.V. Buividovich, D. Smith, L. von Smekal (2020). arXiv:2012.05184

  63. T. Brauner, G. Filios, H. Kolešová, Phys. Rev. Lett. 123, 012001 (2019). arXiv:1902.07522

  64. A.P. Balachandran, S. Digal, T. Matsuura, Phys. Rev. D 73, 074009 (2006). arXiv:hep-ph/0509276

  65. A. Yamamoto, PTEP 2018, 103B03 (2018). arXiv:1804.08051

  66. A. Yamamoto, Phys. Rev. Lett. 110, 112001 (2013). arXiv:1210.8250

  67. E. Shintani, S. Aoki, N. Ishizuka, K. Kanaya, Y. Kikukawa, Y. Kuramashi, M. Okawa, A. Ukawa, T. Yoshie, Phys. Rev. D 75, 034507 (2007). arXiv:hep-lat/0611032

  68. E. Shintani, S. Aoki, Y. Kuramashi, Phys. Rev. D 78, 014503 (2008). arXiv:0803.0797

  69. H.R. Fiebig, W. Wilcox, R.M. Woloshyn, Nucl. Phys. B 324, 47 (1989)

    Article  ADS  Google Scholar 

  70. J.C. Christensen, W. Wilcox, F.X. Lee, L.m. Zhou, Phys. Rev. D 72, 034503 (2005). arXiv:hep-lat/0408024

  71. M. Engelhardt (LHPC), Phys. Rev. D 76, 114502 (2007). arXiv:0706.3919

  72. W. Detmold, B.C. Tiburzi, A. Walker-Loud, Phys. Rev. D 79, 094505 (2009). arXiv:0904.1586

  73. W. Detmold, B.C. Tiburzi, A. Walker-Loud, Phys. Rev. D 81, 054502 (2010). arXiv:1001.1131

  74. M. D’Elia, M. Mariti, F. Negro, Phys. Rev. Lett. 110, 082002 (2013). arXiv:1209.0722

  75. J. Schwinger, Phys. Rev. 82, 664 (1951)

    Article  ADS  MathSciNet  Google Scholar 

  76. L.E. Parker, D. Toms, Quantum Field Theory in Curved Spacetime: Quantized Field and Gravity, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, 2009)

    Book  Google Scholar 

  77. A. Yamamoto, Y. Hirono, Phys. Rev. Lett. 111, 081601 (2013). arXiv:1303.6292

  78. J. Jersak, C.B. Lang, T. Neuhaus, Phys. Rev. Lett. 77, 1933 (1996). arXiv:hep-lat/9606010

  79. I. Campos, A. Cruz, A. Tarancon, Nucl. Phys. B 528, 325 (1998). arXiv:hep-lat/9803007

    Article  ADS  Google Scholar 

  80. M. Hayakawa, H. So, H. Suzuki, Prog. Theor. Phys. 116, 197 (2006). arXiv:hep-lat/0604003

    Article  ADS  Google Scholar 

  81. M. Trencseni (2012). arXiv:1208.4990

  82. A. Yamamoto, Phys. Rev. D 90, 054510 (2014). arXiv:1405.6665

  83. K.H. Villegas, J.P. Esguerra, Mod. Phys. Lett. A 30, 1550020 (2015). arXiv:1407.1371

  84. S. Benić, A. Yamamoto, Phys. Rev. D 93, 094505 (2016). arXiv:1603.00716

  85. V.V. Braguta, A.Y. Kotov, D.D. Kuznedelev, A.A. Roenko, JETP Lett. 112, 6 (2020)

    Article  ADS  Google Scholar 

  86. V.V. Braguta, A.Y. Kotov, D.D. Kuznedelev, A.A. Roenko (2021). arXiv:2102.05084

  87. H. Kleinert, Gauge fields in condensed matter. Vol. II: Stresses and defects. Differential geometry, crystal melting (World Scientific, Singapore, 1989)

  88. S. Imaki, A. Yamamoto, Phys. Rev. D 100, 054509 (2019). arXiv:1906.02406

  89. D. Kharzeev, A. Zhitnitsky, Nucl. Phys. A 797, 67 (2007). arXiv:0706.1026

    Article  ADS  Google Scholar 

  90. D.T. Son, P. Surowka, Phys. Rev. Lett. 103, 191601 (2009). arXiv:0906.5044

  91. Z.V. Khaidukov, M.A. Zubkov, JETP Lett. 108, 670 (2018). arXiv:1812.00970

    Article  ADS  Google Scholar 

  92. S. Imaki, Z. Qiu, Phys. Rev. D 102, 016001 (2020). arXiv:2004.11899

Download references

Acknowledgements

The author was supported by JSPS KAKENHI Grant No. 19K03841.

Author information

Authors and Affiliations

  1. Department of Physics, The University of Tokyo, Tokyo, 113-0033, Japan

    Arata Yamamoto

Authors
  1. Arata Yamamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Carsten Urbach

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yamamoto, A. Overview of external electromagnetism and rotation in lattice QCD. Eur. Phys. J. A 57, 211 (2021). https://doi.org/10.1140/epja/s10050-021-00530-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epja/s10050-021-00530-8

Search

Navigation