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Anomalous electrodynamics of neutral pion matter in strong magnetic fields

  • Tomáš BraunerEmail author
  • Saurabh V. Kadam
Open Access
Regular Article - Theoretical Physics

Abstract

The ground state of quantum chromodynamics in sufficiently strong external magnetic fields and at moderate baryon chemical potential is a chiral soliton lattice (CSL) of neutral pions [1]. We investigate the interplay between the CSL structure and dynamical electromagnetic fields. Our main result is that in presence of the CSL background, the two physical photon polarizations and the neutral pion mix, giving rise to two gapped excitations and one gapless mode with a nonrelativistic dispersion relation. The nature of this mode depends on the direction of its propagation, interpolating between a circularly polarized electromagnetic wave [2] and a neutral pion surface wave, which in turn arises from the spontaneously broken translation invariance. Quite remarkably, there is a neutral-pion-like mode that remains gapped even in the chiral limit, in seeming contradiction to the Goldstone theorem. Finally, we have a first look at the effect of thermal fluctuations of the CSL, showing that even the soft nonrelativistic excitation does not lead to the Landau-Peierls instability. However, it leads to an anomalous contribution to pressure that scales with temperature and magnetic field as T 5/2(B/f π )3/2.

Keywords

Phase Diagram of QCD Topological States of Matter Effective Field Theories 

Notes

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.

References

  1. [1]
    T. Brauner and N. Yamamoto, Chiral soliton lattice and charged pion condensation in strong magnetic fields, arXiv:1609.05213 [INSPIRE].
  2. [2]
    N. Yamamoto, Axion electrodynamics and nonrelativistic photons in nuclear and quark matter, Phys. Rev. D 93 (2016) 085036 [arXiv:1512.05668] [INSPIRE].ADSGoogle Scholar
  3. [3]
    J.O. Andersen, W.R. Naylor and A. Tranberg, Phase diagram of QCD in a magnetic field: a review, Rev. Mod. Phys. 88 (2016) 025001 [arXiv:1411.7176] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    D.T. Son and M.A. Stephanov, Axial anomaly and magnetism of nuclear and quark matter, Phys. Rev. D 77 (2008) 014021 [arXiv:0710.1084] [INSPIRE].ADSGoogle Scholar
  5. [5]
    I.E. Dzyaloshinsky, Theory of helicoidal structures in antiferromagnets. I. Nonmetals, Sov. Phys. JETP 19 (1964) 960 [Zh. Eksp. Teor. Fiz. 46 (1964) 1420].Google Scholar
  6. [6]
    P.G. De Gennes, Calcul de la distorsion d’une structure cholesterique par un champ magnetique (in French), Solid State Commun. 6 (1968) 163.ADSCrossRefGoogle Scholar
  7. [7]
    Z. Qiu, G. Cao and X.-G. Huang, On electrodynamics of chiral matter, Phys. Rev. D 95 (2017) 036002 [arXiv:1612.06364] [INSPIRE].ADSGoogle Scholar
  8. [8]
    S. Ozaki and N. Yamamoto, Axion crystals, arXiv:1610.07835 [INSPIRE].
  9. [9]
    J. Gasser and H. Leutwyler, Chiral perturbation theory to one loop, Annals Phys. 158 (1984) 142 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    F. Wilczek, Two applications of axion electrodynamics, Phys. Rev. Lett. 58 (1987) 1799 [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    M. Alford and K. Rajagopal, Absence of two flavor color superconductivity in compact stars, JHEP 06 (2002) 031 [hep-ph/0204001] [INSPIRE].
  12. [12]
    J.-I. Kishine and A.S. Ovchinnikov, Theory of monoaxial chiral helimagnet, Solid State Phys. 66 (2015) 1.CrossRefGoogle Scholar
  13. [13]
    I. Low and A.V. Manohar, Spontaneously broken space-time symmetries and Goldstone’s theorem, Phys. Rev. Lett. 88 (2002) 101602 [hep-th/0110285] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    H. Watanabe and H. Murayama, Nambu-Goldstone bosons with fractional-power dispersion relations, Phys. Rev. D 89 (2014) 101701 [arXiv:1403.3365] [INSPIRE].ADSGoogle Scholar
  15. [15]
    M. Abramowitz and I.A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards, U.S.A., (1972).zbMATHGoogle Scholar
  16. [16]
    S. Flügge, Practical quantum mechanics, Springer, Berlin Heidelberg Germany, (1999).zbMATHGoogle Scholar
  17. [17]
    H. Watanabe and H. Murayama, Redundancies in Nambu-Goldstone bosons, Phys. Rev. Lett. 110 (2013) 181601 [arXiv:1302.4800] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    T. Hayata and Y. Hidaka, Broken spacetime symmetries and elastic variables, Phys. Lett. B 735 (2014) 195 [arXiv:1312.0008] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    H. Watanabe and H. Murayama, Noncommuting momenta of topological solitons, Phys. Rev. Lett. 112 (2014) 191804 [arXiv:1401.8139] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    M. Kobayashi and M. Nitta, Nonrelativistic Nambu-Goldstone modes associated with spontaneously broken space-time and internal symmetries, Phys. Rev. Lett. 113 (2014) 120403 [arXiv:1402.6826] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    T.-G. Lee, E. Nakano, Y. Tsue, T. Tatsumi and B. Friman, Landau-Peierls instability in a Fulde-Ferrell type inhomogeneous chiral condensed phase, Phys. Rev. D 92 (2015) 034024 [arXiv:1504.03185] [INSPIRE].ADSGoogle Scholar
  22. [22]
    Y. Hidaka, K. Kamikado, T. Kanazawa and T. Noumi, Phonons, pions and quasi-long-range order in spatially modulated chiral condensates, Phys. Rev. D 92 (2015) 034003 [arXiv:1505.00848] [INSPIRE].ADSGoogle Scholar
  23. [23]
    S.R. Coleman, There are no Goldstone bosons in two-dimensions, Commun. Math. Phys. 31 (1973) 259 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    T. Brauner and S. Moroz, Topological interactions of Nambu-Goldstone bosons in quantum many-body systems, Phys. Rev. D 90 (2014) 121701 [arXiv:1405.2670] [INSPIRE].ADSGoogle Scholar
  25. [25]
    J.I. Kapusta and C. Gale, Finite-temperature field theory: principles and applications, Cambridge University Press, Cambridge U.K., (2006).CrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Natural SciencesUniversity of StavangerStavangerNorway
  2. 2.Indian Institute of Science Education and Research (IISER)PuneIndia

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