From physical symmetries to emergent gauge symmetries

  • Carlos Barceló
  • Raúl Carballo-Rubio
  • Francesco Di FilippoEmail author
  • Luis J. Garay
Open Access
Regular Article - Theoretical Physics


Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.


Gauge Symmetry Global Symmetries Models of Quantum Gravity Effective field theories 


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.


  1. [1]
    S. Carlip, Quantum gravity: a progress report, Rept. Prog. Phys. 64 (2001) 885 [gr-qc/0108040] [INSPIRE].
  2. [2]
    T. Thiemann, Modern canonical quantum general relativity, Cambridge University Press (2008).Google Scholar
  3. [3]
    S. Carlip, Challenges for Emergent Gravity, Stud. Hist. Phil. Sci. B 46 (2014) 200 [arXiv:1207.2504] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  4. [4]
    S. Weinberg and E. Witten, Limits on Massless Particles, Phys. Lett. B 96 (1980) 59 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    D. Marolf, Emergent Gravity Requires Kinematic Nonlocality, Phys. Rev. Lett. 114 (2015) 031104 [arXiv:1409.2509] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    G. Baskaran and P.W. Anderson, Gauge theory of high temperature superconductors and strongly correlated Fermi systems, Phys. Rev. B 37 (1988) 580 [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    M. Henneaux and C. Teitelboim, Quantization of gauge systems, Princeton University Press, U.S.A. (1992).zbMATHGoogle Scholar
  8. [8]
    C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, W.H. Freeman, San Francisco U.S.A. (1973).Google Scholar
  9. [9]
    M. Bañados and I.A. Reyes, A short review on Noether’s theorems, gauge symmetries and boundary terms, Int. J. Mod. Phys. D 25 (2016) 1630021 [arXiv:1601.03616] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    A.W. Wipf, Hamilton’s formalism for systems with constraints, hep-th/9312078 [INSPIRE].
  11. [11]
    B. Julia and S. Silva, Currents and superpotentials in classical gauge invariant theories. 1. Local results with applications to perfect fluids and general relativity, Class. Quant. Grav. 15 (1998) 2173 [gr-qc/9804029] [INSPIRE].
  12. [12]
    V. Aldaya, M. Calixto, J. Guerrero and F.F. Lopez-Ruiz, Symmetries of non-linear systems: group approach to their quantization, Int. J. Geom. Meth. Mod. Phys. 8 (2011) 1329 [arXiv:1012.3681] [INSPIRE].MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13]
    C. Barceló, R. Carballo-Rubio, L.J. Garay and G. Jannes, Electromagnetism as an emergent phenomenon: a step-by-step guide, New J. Phys. 16 (2014) 123028 [arXiv:1407.6532] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    C. Itzykson and J.B. Zuber, Quantum Field Theory, Dover Books on Physics, Dover Publications (2012).Google Scholar
  15. [15]
    J. Beltrán Jiménez and A.L. Maroto, Cosmological electromagnetic fields and dark energy, JCAP 03 (2009) 016 [arXiv:0811.0566] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    J. Beltrán Jiménez and A.L. Maroto, The electromagnetic dark sector, Phys. Lett. B 686 (2010) 175 [arXiv:0903.4672] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    J. Beltrán Jiménez and A.L. Maroto, Dark energy: the absolute electric potential of the universe, Int. J. Mod. Phys. D 18 (2009) 2243 [arXiv:0905.2589] [INSPIRE].MathSciNetzbMATHCrossRefGoogle Scholar
  18. [18]
    J. Beltrán Jiménez and A.L. Maroto, The Dark Magnetism of the Universe, Mod. Phys. Lett. A 26 (2011) 3025 [arXiv:1112.1106] [INSPIRE].zbMATHCrossRefGoogle Scholar
  19. [19]
    S. Weinberg, Gravitation and Cosmology: principles and applications of the general theory of relativity, John Wiley and Sons, New York U.S.A (1972).Google Scholar
  20. [20]
    D. Colladay and V.A. Kostelecky, Lorentz violating extension of the standard model, Phys. Rev. D 58 (1998) 116002 [hep-ph/9809521] [INSPIRE].
  21. [21]
    V.A. Kostelecky, Gravity, Lorentz violation and the standard model, Phys. Rev. D 69 (2004) 105009 [hep-th/0312310] [INSPIRE].ADSGoogle Scholar
  22. [22]
    C. Barceló, S. Liberati and M. Visser, Analogue gravity, Living Rev. Rel. 8 (2005) 12 [gr-qc/0505065] [INSPIRE].
  23. [23]
    F. Girelli, S. Liberati and L. Sindoni, Emergence of Lorentzian signature and scalar gravity, Phys. Rev. D 79 (2009) 044019 [arXiv:0806.4239] [INSPIRE].ADSGoogle Scholar
  24. [24]
    S. Liberati and L. Maccione, Lorentz violation: motivation and new constraints, Ann. Rev. Nucl. Part. Sci. 59 (2009) 245 [arXiv:0906.0681] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    G. Volovik, Emergent physics: Fermi-point scenario, Philos. T. Roy. Soc. A 366 (2008) 2935 [arXiv:0801.0724] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  26. [26]
    G.E. Volovik, The Universe in a Helium Droplet, International Series of Monographs on Physics, Oxford University Press, Oxford (2009).Google Scholar
  27. [27]
    A. Belenchia, S. Liberati and A. Mohd, Emergent gravitational dynamics in a relativistic Bose-Einstein condensate, Phys. Rev. D 90 (2014) 104015 [arXiv:1407.7896] [INSPIRE].ADSGoogle Scholar
  28. [28]
    J. Collins, A. Perez, D. Sudarsky, L. Urrutia and H. Vucetich, Lorentz invariance and quantum gravity: an additional fine-tuning problem?, Phys. Rev. Lett. 93 (2004) 191301 [gr-qc/0403053] [INSPIRE].
  29. [29]
    R. Gambini, S. Rastgoo and J. Pullin, Small Lorentz violations in quantum gravity: do they lead to unacceptably large effects?, Class. Quant. Grav. 28 (2011) 155005 [arXiv:1106.1417] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  30. [30]
    A. Belenchia, A. Gambassi and S. Liberati, Lorentz violation naturalness revisited, JHEP 06 (2016) 049 [arXiv:1601.06700] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    S. Liberati, S. Sonego and M. Visser, Faster than c signals, special relativity and causality, Annals Phys. 298 (2002) 167 [gr-qc/0107091] [INSPIRE].
  32. [32]
    C. Barceló and G. Jannes, A real Lorentz-FitzGerald contraction, Found. Phys. 38 (2008) 191 [arXiv:0705.4652] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  33. [33]
    F. Loebbert, The Weinberg-Witten theorem on massless particles: an essay, Ann. Phys. 17 (2008) 803 [INSPIRE].zbMATHCrossRefGoogle Scholar
  34. [34]
    S. Deser, Selfinteraction and gauge invariance, Gen. Rel. Grav. 1 (1970) 9 [gr-qc/0411023] [INSPIRE].
  35. [35]
    S. Deser, Gravity from self-interaction redux, Gen. Rel. Grav. 42 (2010) 641 [arXiv:0910.2975] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  36. [36]
    C. Barceló, R. Carballo-Rubio and L.J. Garay, Unimodular gravity and general relativity from graviton self-interactions, Phys. Rev. D 89 (2014) 124019 [arXiv:1401.2941] [INSPIRE].ADSGoogle Scholar
  37. [37]
    M.M. Anber, U. Aydemir and J.F. Donoghue, Breaking Diffeomorphism Invariance and Tests for the Emergence of Gravity, Phys. Rev. D 81 (2010) 084059 [arXiv:0911.4123] [INSPIRE].ADSGoogle Scholar
  38. [38]
    J.F. Donoghue, M.M. Anber and U. Aydemir, Gauge noninvariance as tests of emergent gauge symmetry, in proceedings of the 5th Meeting on CPT and Lorentz Symmetry (CPT 10), Bloomington, Indiana U.S.A., June 28 - July 2 2010, p. 113 [arXiv:1007.5049] [INSPIRE].

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Carlos Barceló
    • 1
  • Raúl Carballo-Rubio
    • 1
    • 2
  • Francesco Di Filippo
    • 1
    • 3
    Email author
  • Luis J. Garay
    • 4
    • 5
  1. 1.Instituto de Astrofísica de Andalucía (IAA-CSIC)GranadaSpain
  2. 2.Laboratory for Quantum Gravity & Strings, Department of Mathematics & Applied MathematicsUniversity of Cape TownRondeboschSouth Africa
  3. 3.Dipartamento di Scienze Fisiche “E.R. Caianiello”Università di SalernoFisciano (SA)Italy
  4. 4.Departamento de Física Teórica IIUniversidad Complutense de MadridMadridSpain
  5. 5.Instituto de Estructura de la Materia (IEM-CSIC)MadridSpain

Personalised recommendations