Skip to main content
SpringerLink
Log in
Book cover

Strongly Interacting Matter in Magnetic Fields pp 181–208Cite as

Lattice QCD Simulations in External Background Fields

  • Chapter

Part of the book series: Lecture Notes in Physics ((LNP,volume 871))

Abstract

We discuss recent results and future prospects regarding the investigation, by lattice simulations, of the non-perturbative properties of QCD and of its phase diagram in presence of magnetic or chromomagnetic background fields. After a brief introduction to the formulation of lattice QCD in presence of external fields, we focus on studies regarding the effects of external fields on chiral symmetry breaking, on its restoration at finite temperature and on deconfinement. We conclude with a few comments regarding the effects of electromagnetic background fields on gluodynamics.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    Of course we assume all particles living on the torus to carry integer multiples of some elementary electric charge, otherwise a consistent quantization of the magnetic field would not be possible.

  2. 2.

    The author thanks G. Endrodi for giving him access to the continuum extrapolated data of [16].

References

  1. M. Abramczyk, T. Blum, G. Petropoulos, R. Zhou, PoS LAT2009, 181 (2009)

    Google Scholar 

  2. N.O. Agasian, S.M. Fedorov, Phys. Lett. B 663, 445 (2008)

    ADS  Google Scholar 

  3. N.O. Agasian, I.A. Shushpanov, Phys. Lett. B 472, 143 (2000)

    ADS  Google Scholar 

  4. M.S. Alam, V.S. Kaplunovsky, A. Kundu, J. High Energy Phys. 1204, 111 (2012)

    ADS  Google Scholar 

  5. T. Albash, V.G. Filev, C.V. Johnson, A. Kundu, J. High Energy Phys. 0807, 080 (2008)

    MathSciNet  ADS  Google Scholar 

  6. A. Alexandru, F.X. Lee, PoS LAT2008, 145 (2008). arXiv:0810.2833 [hep-lat]

    Google Scholar 

  7. A. Alexandru, F.X. Lee, PoS LAT2009, 144 (2009). arXiv:0911.2520 [hep-lat]

    Google Scholar 

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

    MathSciNet  ADS  MATH  Google Scholar 

  9. J.O. Andersen, A. Tranberg, arXiv:1204.3360 [hep-ph]

  10. J.O. Andersen, R. Khan, Phys. Rev. D 85, 065026 (2012)

    ADS  Google Scholar 

  11. S. Antropov, M. Bordag, V. Demchik, V. Skalozub, Int. J. Mod. Phys. A 26, 4831 (2011)

    ADS  MATH  Google Scholar 

  12. M. Asakawa, A. Majumder, B. Muller, Phys. Rev. C 81, 064912 (2010)

    ADS  Google Scholar 

  13. S.S. Avancini, D.P. Menezes, M.B. Pinto, C. Providencia, Phys. Rev. D 85, 091901 (2012)

    ADS  Google Scholar 

  14. A.Y. Babansky, E.V. Gorbar, G.V. Shchepanyuk, Phys. Lett. B 419, 272–278 (1998)

    ADS  Google Scholar 

  15. G.S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S.D. Katz, S. Krieg, A. Schafer, K.K. Szabo, J. High Energy Phys. 1202, 044 (2012)

    ADS  Google Scholar 

  16. G.S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S.D. Katz, A. Schafer, arXiv:1206.4205 [hep-lat]

  17. G.S. Bali, F. Bruckmann, M. Constantinou, M. Costa, G. Endrodi, S.D. Katz, H. Panagopoulos, A. Schaefer, arXiv:1209.6015 [hep-lat]

  18. T. Banks, A. Casher, Nucl. Phys. B 169, 103 (1980)

    MathSciNet  ADS  Google Scholar 

  19. O. Bergman, G. Lifschytz, M. Lippert, Phys. Rev. D 79, 105024 (2009)

    ADS  Google Scholar 

  20. C.W. Bernard, T. Draper, K. Olynyk, M. Rushton, Phys. Rev. Lett. 49, 1076 (1982)

    ADS  Google Scholar 

  21. J.K. Boomsma, D. Boer, Phys. Rev. D 81, 074005 (2010)

    ADS  Google Scholar 

  22. V.V. Braguta, P.V. Buividovich, M.N. Chernodub, M.I. Polikarpov, Phys. Lett. B 718, 667 (2012). arXiv:1104.3767 [hep-lat]

    ADS  Google Scholar 

  23. V.V. Braguta, P.V. Buividovich, T. Kalaydzhyan, S.V. Kuznetsov, M.I. Polikarpov, PoS LAT2010, 190 (2010). arXiv:1011.3795 [hep-lat]

    Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  26. P.V. Buividovich, M.N. Chernodub, E.V. Luschevskaya, M.I. Polikarpov, Phys. Lett. B 682, 484 (2010)

    ADS  Google Scholar 

  27. P.V. Buividovich, M.N. Chernodub, E.V. Luschevskaya, M.I. Polikarpov, Nucl. Phys. B 826, 313 (2010)

    MathSciNet  ADS  MATH  Google Scholar 

  28. P.V. Buividovich, M.N. Chernodub, E.V. Luschevskaya, M.I. Polikarpov, Phys. Rev. D 81, 036007 (2010)

    ADS  Google Scholar 

  29. P. Cea, Int. J. Mod. Phys. D 13, 1917 (2004)

    ADS  MATH  Google Scholar 

  30. P. Cea, L. Cosmai, Phys. Lett. B 264, 415 (1991)

    ADS  Google Scholar 

  31. P. Cea, L. Cosmai, J. High Energy Phys. 0302, 031 (2003)

    ADS  Google Scholar 

  32. P. Cea, L. Cosmai, J. High Energy Phys. 0508, 079 (2005)

    ADS  Google Scholar 

  33. P. Cea, L. Cosmai, M. D’Elia, J. High Energy Phys. 0712, 097 (2007)

    ADS  Google Scholar 

  34. P. Cea, L. Cosmai, M. D’Elia, PoS LAT2006, 062 (2006). hep-lat/0610014

    Google Scholar 

  35. P. Cea, L. Cosmai, M. D’Elia, PoS LAT2007, 295 (2007). arXiv:0710.1449 [hep-lat]

    Google Scholar 

  36. P. Cea, L. Cosmai, M. D’Elia, J. High Energy Phys. 0402, 018 (2004)

    ADS  Google Scholar 

  37. P. Cea, L. Cosmai, A.D. Polosa, Phys. Lett. B 392, 177 (1997)

    ADS  Google Scholar 

  38. B. Chatterjee, H. Mishra, A. Mishra, Phys. Rev. D 84, 014016 (2011)

    ADS  Google Scholar 

  39. M.N. Chernodub, Phys. Rev. D 82, 085011 (2010)

    ADS  Google Scholar 

  40. M.N. Chernodub, Phys. Rev. Lett. 106, 142003 (2011)

    ADS  Google Scholar 

  41. M.N. Chernodub, Phys. Rev. D 86, 107703 (2012). arXiv:1209.3587 [hep-ph]

    ADS  Google Scholar 

  42. T.D. Cohen, D.A. McGady, E.S. Werbos, Phys. Rev. C 76, 055201 (2007)

    ADS  Google Scholar 

  43. P.H. Damgaard, U.M. Heller, Nucl. Phys. B 309, 625 (1988)

    ADS  Google Scholar 

  44. M. D’Elia, S. Mukherjee, F. Sanfilippo, Phys. Rev. D 82, 051501 (2010)

    ADS  Google Scholar 

  45. M. D’Elia, F. Negro, Phys. Rev. D 83, 114028 (2011)

    ADS  Google Scholar 

  46. M. D’Elia, M. Mariti, F. Negro, Phys. Rev. Lett. 110, 082002 (2013). arXiv:1209.0722 [hep-lat]

    ADS  Google Scholar 

  47. W. Detmold, B.C. Tiburzi, A. Walker-Loud, Phys. Rev. D 73, 114505 (2006). hep-lat/0603026

    ADS  Google Scholar 

  48. W. Detmold, B.C. Tiburzi, A. Walker-Loud, Phys. Rev. D 79, 094505 (2009). arXiv:0904.1586 [hep-lat]

    ADS  Google Scholar 

  49. W. Detmold, B.C. Tiburzi, A. Walker-Loud, Phys. Rev. D 81, 054502 (2010). arXiv:1001.1131 [hep-lat]

    ADS  Google Scholar 

  50. R.C. Duncan, C. Thompson, Astrophys. J. 392, L9 (1992)

    ADS  Google Scholar 

  51. D. Ebert, V.V. Khudyakov, V.C. Zhukovsky, K.G. Klimenko, Phys. Rev. D 65, 054024 (2002)

    ADS  Google Scholar 

  52. D. Ebert, K.G. Klimenko, M.A. Vdovichenko, A.S. Vshivtsev, Phys. Rev. D 61, 025005 (2000)

    ADS  Google Scholar 

  53. H.T. Elze, B. Muller, J. Rafelski, hep-ph/9811372

  54. H.T. Elze, J. Rafelski, in Sandansky 1998, Frontier tests of QED and physics of the vacuum, pp. 425–439. hep-ph/9806389

  55. N. Evans, T. Kalaydzhyan, K.-y. Kim, I. Kirsch, J. High Energy Phys. 1101, 050 (2011)

    ADS  Google Scholar 

  56. S. Fayazbakhsh, N. Sadooghi, Phys. Rev. D 83, 025026 (2011)

    ADS  Google Scholar 

  57. G.N. Ferrari, A.F. Garcia, M.B. Pinto, arXiv:1207.3714 [hep-ph]

  58. V.G. Filev, C.V. Johnson, R.C. Rashkov, K.S. Viswanathan, J. High Energy Phys. 0710, 019 (2007)

    ADS  Google Scholar 

  59. E.S. Fraga, A.J. Mizher, Phys. Rev. D 78, 025016 (2008)

    ADS  Google Scholar 

  60. E.S. Fraga, L.F. Palhares, Phys. Rev. D 86, 016008 (2012). arXiv:1201.5881 [hep-ph]

    ADS  Google Scholar 

  61. E.S. Fraga, J. Noronha, L.F. Palhares, arXiv:1207.7094 [hep-ph]

  62. K. Fukushima, Y. Hidaka, arXiv:1209.1319 [hep-ph]

  63. K. Fukushima, D.E. Kharzeev, H.J. Warringa, Phys. Rev. D 78, 074033 (2008)

    ADS  Google Scholar 

  64. K. Fukushima, J.M. Pawlowski, arXiv:1203.4330 [hep-ph]

  65. K. Fukushima, M. Ruggieri, R. Gatto, Phys. Rev. D 81, 114031 (2010)

    ADS  Google Scholar 

  66. B.V. Galilo, S.N. Nedelko, Phys. Rev. D 84, 094017 (2011)

    ADS  Google Scholar 

  67. R. Gatto, M. Ruggieri, Phys. Rev. D 82, 054027 (2010)

    ADS  Google Scholar 

  68. R. Gatto, M. Ruggieri, Phys. Rev. D 83, 034016 (2011)

    ADS  Google Scholar 

  69. R. Gatto, M. Ruggieri, arXiv:1207.3190 [hep-ph]

  70. A. Goyal, M. Dahiya, Phys. Rev. D 62, 025022 (2000)

    ADS  Google Scholar 

  71. V.P. Gusynin, V.A. Miransky, I.A. Shovkovy, Phys. Rev. Lett. 73, 3499 (1994). [Erratum. Phys. Rev. Lett. 76, 1005 (1996)]

    ADS  Google Scholar 

  72. V.P. Gusynin, V.A. Miransky, I.A. Shovkovy, Phys. Lett. B 349, 477 (1995)

    ADS  Google Scholar 

  73. Y. Hidaka, A. Yamamoto, arXiv:1209.0007 [hep-ph]

  74. E.-M. Ilgenfritz, M. Kalinowski, M. Muller-Preussker, B. Petersson, A. Schreiber, Phys. Rev. D 85, 114504 (2012)

    ADS  Google Scholar 

  75. D.N. Kabat, K.-M. Lee, E.J. Weinberg, Phys. Rev. D 66, 014004 (2002)

    ADS  Google Scholar 

  76. K. Kashiwa, Phys. Rev. D 83, 117901 (2011)

    ADS  Google Scholar 

  77. S. Kawati, G. Konisi, H. Miyata, Phys. Rev. D 28, 1537–1541 (1983)

    ADS  Google Scholar 

  78. D.E. Kharzeev, L.D. McLerran, H.J. Warringa, Nucl. Phys. A 803, 227 (2008)

    ADS  Google Scholar 

  79. S.P. Klevansky, R.H. Lemmer, Phys. Rev. D 39, 3478 (1989)

    ADS  Google Scholar 

  80. K.G. Klimenko, Z. Phys. C 54, 323 (1992)

    MathSciNet  ADS  Google Scholar 

  81. K.G. Klimenko, Theor. Math. Phys. 94, 393 (1993)

    MATH  Google Scholar 

  82. K.G. Klimenko, B.V. Magnitsky, A.S. Vshivtsev, Nuovo Cimento A 107, 439–452 (1994)

    ADS  Google Scholar 

  83. C.V. Johnson, A. Kundu, J. High Energy Phys. 0812, 053 (2008)

    MathSciNet  ADS  Google Scholar 

  84. A.D. Linde, Phys. Lett. B 62, 435 (1976)

    ADS  Google Scholar 

  85. M. Luscher, R. Narayanan, P. Weisz, U. Wolff, Nucl. Phys. B 384, 168 (1992)

    MathSciNet  ADS  Google Scholar 

  86. M. Luscher, P. Weisz, Nucl. Phys. B 452, 213 (1995)

    MathSciNet  ADS  Google Scholar 

  87. E.V. Luschevskaya, O.V. Larina, arXiv:1203.5699 [hep-lat]

  88. G. Martinelli, G. Parisi, R. Petronzio, F. Rapuano, Phys. Lett. B 116, 434 (1982)

    ADS  Google Scholar 

  89. S. Mereghetti, Astron. Astrophys. Rev. 15, 225–287 (2008)

    ADS  Google Scholar 

  90. V.A. Miransky, I.A. Shovkovy, Phys. Rev. D 66, 045006 (2002)

    ADS  Google Scholar 

  91. A.J. Mizher, M.N. Chernodub, E.S. Fraga, Phys. Rev. D 82, 105016 (2010)

    ADS  Google Scholar 

  92. M.M. Musakhanov, F.C. Khanna, hep-ph/9605232

  93. S.-i. Nam, C.-W. Kao, Phys. Rev. D 83, 096009 (2011)

    ADS  Google Scholar 

  94. F. Preis, A. Rebhan, A. Schmitt, J. High Energy Phys. 1103, 033 (2011)

    ADS  Google Scholar 

  95. F. Preis, A. Rebhan, A. Schmitt, J. Phys. G 39, 054006 (2012). arXiv:1209.4468 [hep-ph]

    ADS  Google Scholar 

  96. A. Rabhi, C. Providencia, Phys. Rev. C 83, 055801 (2011)

    ADS  Google Scholar 

  97. E. Rojas, A. Ayala, A. Bashir, A. Raya, Phys. Rev. D 77, 093004 (2008)

    ADS  Google Scholar 

  98. A. Salam, J.A. Strathdee, Nucl. Phys. B 90, 203 (1975)

    MathSciNet  ADS  Google Scholar 

  99. S. Schramm, B. Muller, A.J. Schramm, Mod. Phys. Lett. A 7, 973–982 (1992)

    ADS  Google Scholar 

  100. E. Shintani, S. Aoki, N. Ishizuka, K. Kanaya, Y. Kikukawa, Y. Kuramashi, M. Okawa, A. Ukawa et al., Phys. Rev. D 75, 034507 (2007)

    ADS  Google Scholar 

  101. I.A. Shovkovy, arXiv:1207.5081 [hep-ph]

  102. I.A. Shushpanov, A.V. Smilga, Phys. Lett. B 402, 351 (1997)

    ADS  Google Scholar 

  103. V. Skokov, Phys. Rev. D 85, 034026 (2012)

    ADS  Google Scholar 

  104. V. Skokov, A.Y. Illarionov, V. Toneev, Int. J. Mod. Phys. A 24, 5925 (2009)

    ADS  Google Scholar 

  105. J. Smit, J.C. Vink, Nucl. Phys. B 286, 485 (1987)

    MathSciNet  ADS  Google Scholar 

  106. H. Suganuma, T. Tatsumi, Ann. Phys. 208, 470 (1991)

    ADS  Google Scholar 

  107. G. ’t Hooft, Nucl. Phys. B 153, 141 (1979)

    ADS  Google Scholar 

  108. B.C. Tiburzi, PoS LAT2011, 020 (2011). arXiv:1110.6842 [hep-lat]

    Google Scholar 

  109. B.C. Tiburzi, Nucl. Phys. A 814, 74 (2008)

    ADS  Google Scholar 

  110. B.C. Tiburzi, Phys. Lett. B 674, 336 (2009)

    ADS  Google Scholar 

  111. T. Vachaspati, Phys. Lett. B 265, 258 (1991)

    ADS  Google Scholar 

  112. A. Vilenkin, Phys. Rev. D 22, 3080 (1980)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  114. A. Yamamoto, Phys. Rev. Lett. 107, 031601 (2011)

    ADS  Google Scholar 

  115. A.V. Zayakin, J. High Energy Phys. 0807, 116 (2008)

    MathSciNet  ADS  Google Scholar 

Download references

Acknowledgements

The author is grateful to P. Cea, L. Cosmai, M. Mariti, S. Mukherjee, F. Negro and F. Sanfilippo for collaboration on some of topics discussed in this review. He also acknowledges M. Chernodub, G. Endrodi, E. Fraga, K. Fukushima, V. Miransky and M. Ruggieri for many useful discussions.

Author information

Authors and Affiliations

  1. Dipartimento di Fisica dell’Università di Pisa and INFN—Sezione di Pisa, Largo Pontecorvo 3, I-56127, Pisa, Italy

    Massimo D’Elia

Authors
  1. Massimo D’Elia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Massimo D’Elia .

Editor information

Editors and Affiliations

  1. Department of Physics, Stony Brook University, Nicolls Rd 100, Stony Brook, 11794, New York, USA

    Dmitri Kharzeev

  2. Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, Nicolas Cabrera 13-15, Madrid, 28049, Spain

    Karl Landsteiner

  3. Institut für Theoretische Physik, Technische Universität Wien, Wiedner Haupstr. 8, Wien, 1040, Austria

    Andreas Schmitt

  4. Physics Department (MC 273), University of Illinois at Chicago, West Taylor Street 845Rm 2236, Chicago, 60607, Illinois, USA

    Ho-Ung Yee

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

D’Elia, M. (2013). Lattice QCD Simulations in External Background Fields. In: Kharzeev, D., Landsteiner, K., Schmitt, A., Yee, HU. (eds) Strongly Interacting Matter in Magnetic Fields. Lecture Notes in Physics, vol 871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37305-3_7

Download citation

Publish with us

Policies and ethics

Search

Navigation