Abstract
We analyze the mechanism of spontaneous symmetry breaking of scale invariance in Galilean invariant field theories. We show that the existence of a dynamic gapless dilaton mode depends on whether the U(1) particle number or the Galilean boost symmetry are spontaneously broken. When both scale and particle number symmetries are spontaneously broken there is one propagating gapless Nambu-Goldstone mode. Its dispersion relation is linear if the chemical potential is nonzero and quadratic otherwise. We discuss the reversibility of RG flows in such theories.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Y. Nambu, Quasiparticles and Gauge Invariance in the Theory of Superconductivity, Phys. Rev. 117 (1960) 648.
J. Goldstone, Field Theories with Superconductor Solutions, Nuovo Cim. 19 (1961) 154.
J. Goldstone, A. Salam and S. Weinberg, Broken Symmetries, Phys. Rev. 127 (1962) 965.
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, Redundancies in Nambu-Goldstone Bosons, Phys. Rev. Lett. 110 (2013) 181601 [arXiv:1302.4800] [INSPIRE].
H.B. Nielsen and S. Chadha, On How to Count Goldstone Bosons, Nucl. Phys. B 105 (1976) 445 [INSPIRE].
H. Watanabe and H. Murayama, Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance, Phys. Rev. Lett. 108 (2012) 251602 [arXiv:1203.0609] [INSPIRE].
A. Nicolis and F. Piazza, Implications of Relativity on Nonrelativistic Goldstone Theorems: Gapped Excitations at Finite Charge Density, Phys. Rev. Lett. 110 (2013) 011602 [Addendum ibid. 110 (2013) 039901] [arXiv:1204.1570] [INSPIRE].
Z. Komargodski and A. Schwimmer, On Renormalization Group Flows in Four Dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987] [INSPIRE].
D.T. Son, Toward an AdS/cold atoms correspondence: A Geometric realization of the Schrödinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [INSPIRE].
E.A. Ivanov and V.I. Ogievetsky, The Inverse Higgs Phenomenon in Nonlinear Realizations, Teor. Mat. Fiz. 25 (1975) 164 [INSPIRE].
T. Brauner and H. Watanabe, Spontaneous breaking of spacetime symmetries and the inverse Higgs effect, Phys. Rev. D 89 (2014) 085004 [arXiv:1401.5596] [INSPIRE].
A. Nicolis, R. Penco, F. Piazza and R.A. Rosen, More on gapped Goldstones at finite density: More gapped Goldstones, JHEP 11 (2013) 055 [arXiv:1306.1240] [INSPIRE].
S. Endlich, A. Nicolis and R. Penco, Spontaneously broken mass, JHEP 01 (2015) 146 [arXiv:1310.2272] [INSPIRE].
A. Nicolis, R. Penco, F. Piazza and R. Rattazzi, Zoology of condensed matter: Framids, ordinary stuff, extra-ordinary stuff, JHEP 06 (2015) 155 [arXiv:1501.03845] [INSPIRE].
S. Lellouch, T. Dao, T. Koffel, and L. Sanchez-Palencia, Two-component Bose gases with one-body and two-body couplings, Phys. Rev. A 88 (2013) 063646 [arXiv:1307.0488].
A. Schwimmer and S. Theisen, Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching, Nucl. Phys. B 847 (2011) 590 [arXiv:1011.0696] [INSPIRE].
K. Jensen, On the coupling of Galilean-invariant field theories to curved spacetime, arXiv:1408.6855 [INSPIRE].
D.T. Son and M. Wingate, General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas, Annals Phys. 321 (2006) 197 [cond-mat/0509786] [INSPIRE].
I. Arav, S. Chapman and Y. Oz, Non-Relativistic Scale Anomalies, JHEP 06 (2016) 158 [arXiv:1601.06795] [INSPIRE].
M. Baggio, J. de Boer and K. Holsheimer, Anomalous Breaking of Anisotropic Scaling Symmetry in the Quantum Lifshitz Model, JHEP 07 (2012) 099 [arXiv:1112.6416] [INSPIRE].
T. Griffin, P. Hořava and C.M. Melby-Thompson, Conformal Lifshitz Gravity from Holography, JHEP 05 (2012) 010 [arXiv:1112.5660] [INSPIRE].
I. Arav, S. Chapman and Y. Oz, Lifshitz Scale Anomalies, JHEP 02 (2015) 078 [arXiv:1410.5831] [INSPIRE].
R. Auzzi, S. Baiguera and G. Nardelli, On Newton-Cartan trace anomalies, JHEP 02 (2016) 003 [Erratum ibid. 02 (2016) 177] [arXiv:1511.08150] [INSPIRE].
R. Auzzi, S. Baiguera, F. Filippini and G. Nardelli, On Newton-Cartan local renormalization group and anomalies, JHEP 11 (2016) 163 [arXiv:1610.00123] [INSPIRE].
I. Arav, Y. Oz and A. Raviv-Moshe, Lifshitz Anomalies, Ward Identities and Split Dimensional Regularization, JHEP 03 (2017) 088 [arXiv:1612.03500] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1702.00690
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Arav, I., Hason, I. & Oz, Y. Spontaneous breaking of non-relativistic scale symmetry. J. High Energ. Phys. 2017, 63 (2017). https://doi.org/10.1007/JHEP10(2017)063
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2017)063