From physical symmetries to emergent gauge symmetries


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.

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  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).

  3. [3]

    S. Carlip, Challenges for Emergent Gravity, Stud. Hist. Phil. Sci. B 46 (2014) 200 [arXiv:1207.2504] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  4. [4]

    S. Weinberg and E. Witten, Limits on Massless Particles, Phys. Lett. B 96 (1980) 59 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  5. [5]

    D. Marolf, Emergent Gravity Requires Kinematic Nonlocality, Phys. Rev. Lett. 114 (2015) 031104 [arXiv:1409.2509] [INSPIRE].

    ADS  Article  Google 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].

    ADS  Article  Google Scholar 

  7. [7]

    M. Henneaux and C. Teitelboim, Quantization of gauge systems, Princeton University Press, U.S.A. (1992).

    MATH  Google Scholar 

  8. [8]

    C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, W.H. Freeman, San Francisco U.S.A. (1973).

  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].

    ADS  Article  Google 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].

    MathSciNet  MATH  Article  Google 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].

    ADS  Article  Google Scholar 

  14. [14]

    C. Itzykson and J.B. Zuber, Quantum Field Theory, Dover Books on Physics, Dover Publications (2012).

  15. [15]

    J. Beltrán Jiménez and A.L. Maroto, Cosmological electromagnetic fields and dark energy, JCAP 03 (2009) 016 [arXiv:0811.0566] [INSPIRE].

    ADS  Article  Google Scholar 

  16. [16]

    J. Beltrán Jiménez and A.L. Maroto, The electromagnetic dark sector, Phys. Lett. B 686 (2010) 175 [arXiv:0903.4672] [INSPIRE].

    ADS  Article  Google 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].

    MathSciNet  MATH  Article  Google 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].

    MATH  Article  Google 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].

    ADS  Google 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].

    ADS  Google 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].

    ADS  Article  Google Scholar 

  25. [25]

    G. Volovik, Emergent physics: Fermi-point scenario, Philos. T. Roy. Soc. A 366 (2008) 2935 [arXiv:0801.0724] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  26. [26]

    G.E. Volovik, The Universe in a Helium Droplet, International Series of Monographs on Physics, Oxford University Press, Oxford (2009).

  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].

    ADS  Google 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].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  30. [30]

    A. Belenchia, A. Gambassi and S. Liberati, Lorentz violation naturalness revisited, JHEP 06 (2016) 049 [arXiv:1601.06700] [INSPIRE].

    ADS  Article  Google 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].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  33. [33]

    F. Loebbert, The Weinberg-Witten theorem on massless particles: an essay, Ann. Phys. 17 (2008) 803 [INSPIRE].

    MATH  Article  Google 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].

    ADS  MathSciNet  MATH  Article  Google 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].

    ADS  Google 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].

    ADS  Google 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].

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Correspondence to Francesco Di Filippo.

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Barceló, C., Carballo-Rubio, R., Di Filippo, F. et al. From physical symmetries to emergent gauge symmetries. J. High Energ. Phys. 2016, 84 (2016).

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  • Gauge Symmetry
  • Global Symmetries
  • Models of Quantum Gravity
  • Effective field theories