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.
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References
T. Brauner and N. Yamamoto, Chiral soliton lattice and charged pion condensation in strong magnetic fields, arXiv:1609.05213 [INSPIRE].
N. Yamamoto, Axion electrodynamics and nonrelativistic photons in nuclear and quark matter, Phys. Rev. D 93 (2016) 085036 [arXiv:1512.05668] [INSPIRE].
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].
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].
I.E. Dzyaloshinsky, Theory of helicoidal structures in antiferromagnets. I. Nonmetals, Sov. Phys. JETP 19 (1964) 960 [Zh. Eksp. Teor. Fiz. 46 (1964) 1420].
P.G. De Gennes, Calcul de la distorsion d’une structure cholesterique par un champ magnetique (in French), Solid State Commun. 6 (1968) 163.
Z. Qiu, G. Cao and X.-G. Huang, On electrodynamics of chiral matter, Phys. Rev. D 95 (2017) 036002 [arXiv:1612.06364] [INSPIRE].
S. Ozaki and N. Yamamoto, Axion crystals, arXiv:1610.07835 [INSPIRE].
J. Gasser and H. Leutwyler, Chiral perturbation theory to one loop, Annals Phys. 158 (1984) 142 [INSPIRE].
F. Wilczek, Two applications of axion electrodynamics, Phys. Rev. Lett. 58 (1987) 1799 [INSPIRE].
M. Alford and K. Rajagopal, Absence of two flavor color superconductivity in compact stars, JHEP 06 (2002) 031 [hep-ph/0204001] [INSPIRE].
J.-I. Kishine and A.S. Ovchinnikov, Theory of monoaxial chiral helimagnet, Solid State Phys. 66 (2015) 1.
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].
H. Watanabe and H. Murayama, Nambu-Goldstone bosons with fractional-power dispersion relations, Phys. Rev. D 89 (2014) 101701 [arXiv:1403.3365] [INSPIRE].
M. Abramowitz and I.A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards, U.S.A., (1972).
S. Flügge, Practical quantum mechanics, Springer, Berlin Heidelberg Germany, (1999).
H. Watanabe and H. Murayama, Redundancies in Nambu-Goldstone bosons, Phys. Rev. Lett. 110 (2013) 181601 [arXiv:1302.4800] [INSPIRE].
T. Hayata and Y. Hidaka, Broken spacetime symmetries and elastic variables, Phys. Lett. B 735 (2014) 195 [arXiv:1312.0008] [INSPIRE].
H. Watanabe and H. Murayama, Noncommuting momenta of topological solitons, Phys. Rev. Lett. 112 (2014) 191804 [arXiv:1401.8139] [INSPIRE].
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].
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].
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].
S.R. Coleman, There are no Goldstone bosons in two-dimensions, Commun. Math. Phys. 31 (1973) 259 [INSPIRE].
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].
J.I. Kapusta and C. Gale, Finite-temperature field theory: principles and applications, Cambridge University Press, Cambridge U.K., (2006).
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Brauner, T., Kadam, S.V. Anomalous electrodynamics of neutral pion matter in strong magnetic fields. J. High Energ. Phys. 2017, 15 (2017). https://doi.org/10.1007/JHEP03(2017)015
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DOI: https://doi.org/10.1007/JHEP03(2017)015