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de Sitter gauge theories and induced gravities

  • Regular Article - Theoretical Physics
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Abstract

Pure de Sitter, anti de Sitter, and orthogonal gauge theories in four-dimensional Euclidean spacetime are studied. It is shown that, if the theory is asymptotically free and a dynamical mass is generated, then an effective geometry may be induced and a gravity theory emerges. The asymptotic freedom and the running of the mass might account for an Inönü–Wigner contraction which induces a breaking of the gauge group to the Lorentz group, while the mass itself is responsible for the coset sector of the gauge field to be identified with the effective vierbein. Furthermore, the resulting local isometries are Lorentzian for the anti de Sitter group and Euclidean for the de Sitter and orthogonal groups.

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References

  1. R. Utiyama, Invariant theoretical interpretation of interaction. Phys. Rev. 101, 1597 (1956)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  2. T.W.B. Kibble, Lorentz invariance and the gravitational field. J. Math. Phys. 2, 212 (1961)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  3. D.W. Sciama, The physical structure of general relativity. Rev. Mod. Phys. 36, 463–469 (1964)

    Article  ADS  Google Scholar 

  4. A. Mardones, J. Zanelli, Lovelock–Cartan theory of gravity. Class. Quantum Gravity 8, 1545 (1991)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  5. J. Zanelli, Lecture Notes on Chern–Simons (Super-)Gravities, 2nd edn. (February 2008)

    Google Scholar 

  6. G. ’t Hooft, M.J.G. Veltman, One loop divergencies in the theory of gravitation. Ann. Inst. Henri Poincaré, Phys Teor. A 20, 69–94 (1974)

    MathSciNet  ADS  Google Scholar 

  7. S. Deser, P. van Nieuwenhuizen, One loop divergences of quantized Einstein-Maxwell fields. Phys. Rev. D 10, 401 (1974)

    Article  ADS  Google Scholar 

  8. S. Deser, P. van Nieuwenhuizen, Nonrenormalizability of the quantized Dirac-Einstein system. Phys. Rev. D 10, 411 (1974)

    Article  MathSciNet  ADS  Google Scholar 

  9. K.S. Stelle, P.C. West, De Sitter gauge invariance and the geometry of the Einstein-Cartan theory. J. Phys. A 12, L205–L210 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  10. K.S. Stelle, P.C. West, Spontaneously broken De Sitter symmetry and the gravitational holonomy group. Phys. Rev. D 21, 1466 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  11. A.A. Tseytlin, On the Poincare and De Sitter gauge theories of gravity with propagating torsion. Phys. Rev. D 26, 3327 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  12. F.W. Hehl, G.D. Kerlick, P. Von Der Heyde, On a new metric affine theory of gravitation. Phys. Lett. B 63, 446 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  13. S.W. MacDowell, F. Mansouri, Unified geometric theory of gravity and supergravity. Phys. Rev. Lett. 38, 739 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  14. H.R. Pagels, Gravitational gauge fields and the cosmological constant. Phys. Rev. D 29, 1690 (1984)

    Article  ADS  Google Scholar 

  15. P. Mahato, De Sitter group and Einstein–Hilbert Lagrangian. Phys. Rev. D 70, 124024 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  16. R. Tresguerres, Dynamically broken anti-de Sitter action for gravity. Int. J. Geom. Methods Mod. Phys. 5, 171–183 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. E.W. Mielke, Einsteinian gravity from a spontaneously broken topological BF theory. Phys. Lett. B 688, 273–277 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  18. L. Sindoni, Emergent models for gravity: an overview. arXiv:1110.0686 [gr-qc]

  19. S. Kolekar, T. Padmanabhan, Action principle for the fluid-gravity correspondence and emergent gravity. Phys. Rev. D 85, 024004 (2012)

    Article  ADS  Google Scholar 

  20. R.F. Sobreiro, V.J. Vasquez Otoya, Effective gravity from a quantum gauge theory in Euclidean space-time. Class. Quantum Gravity 24, 4937 (2007)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  21. R.F. Sobreiro, V.J. Vasquez Otoya, On the topological reduction from the affine to the orthogonal gauge theory of gravity. J. Geom. Phys. 61, 137–150 (2011)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  22. R.F. Sobreiro, V.J.V. Otoya, Affine gauge theory of gravity and its reduction to the Riemann-Cartan geometry. J. Phys. Conf. Ser. 283, 012032 (2011)

    Article  ADS  Google Scholar 

  23. O. Piguet, S.P. Sorella, Algebraic Renormalization: Perturbative Renormalization, Symmetries and Anomalies. Springer Lect. Notes Phys., vol. M28 (1995)

    MATH  Google Scholar 

  24. D.J. Gross, F. Wilczek, Ultraviolet behavior of non-Abelian gauge theories. Phys. Rev. Lett. 30, 1343 (1973)

    Article  ADS  Google Scholar 

  25. H.D. Politzer, Reliable perturbative results for strong interactions? Phys. Rev. Lett. 30, 1346 (1973)

    Article  ADS  Google Scholar 

  26. V.N. Gribov, Quantization of nonabelian gauge theories. Nucl. Phys. B 139, 1 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  27. D. Zwanziger, Renormalizability of the critical limit of lattice gauge theory by BRS invariance. Nucl. Phys. B 399, 477–513 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  28. R.F. Sobreiro, S.P. Sorella, Introduction to the Gribov ambiguities in Euclidean Yang–Mills theories. Lectures given by S.P. Sorella at the 13th Jorge Andre Swieca Summer School on Particles and Fields, Campos de Jordão, Brazil, 9–22 January 2005

  29. D. Dudal, R.F. Sobreiro, S.P. Sorella, H. Verschelde, The Gribov parameter and the dimension two gluon condensate in Euclidean Yang–Mills theories in the Landau gauge. Phys. Rev. D 72, 014016 (2005)

    Article  ADS  Google Scholar 

  30. A.C. Aguilar, A. Doff, A.A. Natale, Vacuum energy as a c-function for theories with dynamically generated masses. Phys. Lett. B 696, 173–177 (2011)

    Article  ADS  Google Scholar 

  31. D. Dudal, S.P. Sorella, N. Vandersickel, The dynamical origin of the refinement of the Gribov-Zwanziger theory. Phys. Rev. D 84, 065039 (2011)

    Article  ADS  Google Scholar 

  32. E. Inönü, E.P. Wigner, On the contraction of groups and their representations. Proc. Natl. Acad. Sci. 39, 510–524 (1953)

    Article  MATH  ADS  Google Scholar 

  33. M. Daniel, C.M. Viallet, The geometrical setting of gauge theories of the Yang–Mills type. Rev. Mod. Phys. 52, 175 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  34. A. Trautman, Fiber bundles, gauge fields, and gravitation, in General Relativity and Gravitation, vol. 1, ed. by A. Held (1980), pp. 287–308

    Google Scholar 

  35. M. Nakahara, Geometry, Topology and Physics (Hilger, Bristol, 1990), 505p.

    Book  MATH  Google Scholar 

  36. C. Itzykson, J.B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980), 705p.

    Google Scholar 

  37. Y.N. Obukhov, Gauge fields and space-time geometry. Theor. Math. Phys. 117, 1308–1318 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  38. S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, vol. 1 (Wiley, New York, 1963)

    MATH  Google Scholar 

  39. C. Nash, S. Sen, Topology and Geometry for Physicists (Academic Press, London, 1983), 311p.

    MATH  Google Scholar 

  40. B. McInnes, On the significance of the compatibility condition in gauge theories of the Poincare group. Class. Quantum Gravity 1, 1 (1984)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  41. E.W. Mielke, Weak equivalence principle from a spontaneously broken gauge theory of gravity. Phys. Lett. B 702, 187–190 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  42. J.C. Baez, Four-dimensional BF theory with cosmological term as a topological quantum field theory. Lett. Math. Phys. 38, 129 (1996)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  43. G.T. Horowitz, Exactly soluble diffeomorphism invariant theories. Commun. Math. Phys. 125, 417 (1989)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  44. E.J. Copeland, M. Sami, S. Tsujikawa, Dynamics of dark energy. Int. J. Mod. Phys. D 15, 1753 (2006)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  45. S. Tsujikawa, Dark energy: investigation and modeling. arXiv:1004.1493 [astro-ph.CO]

  46. Y.-Z. Ma, Variable cosmological constant model: its brief review, the reconstruction equation and constraints from supernova data. Nucl. Phys. B 804, 262 (2008)

    Article  ADS  Google Scholar 

  47. L. Perivolaropoulos, Vacuum energy, the cosmological constant, and compact extra dimensions: Constraints from Casimir effect experiments. Phys. Rev. D 77, 107301 (2008)

    Article  ADS  Google Scholar 

  48. E. Komatsu et al. (WMAP Collaboration), Seven-year wilkinson microwave anisotropy probe (WMAP) observations: cosmological interpretation. Astrophys. J. Suppl. 192, 18 (2011)

    Article  ADS  Google Scholar 

  49. O. Luongo, H. Quevedo, Reconstructing the expansion history of the Universe with a one-fluid approach. arXiv:1104.4758 [gr-qc]

  50. O. Luongo, H. Quevedo, An expanding Universe with constant pressure and no cosmological constant. Astrophys. Space Sci. (2011). doi:10.1007/s10509-011-0937-x

  51. I.L. Shapiro, J. Sola, Cosmological constant problems and renormalization group. J. Phys. A 40, 6583 (2007)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  52. I.L. Shapiro, J. Sola, On the possible running of the cosmological constant. Phys. Lett. B 682, 105–113 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  53. A. Cucchieri, T. Mendes, Landau-gauge propagators in Yang–Mills theories at beta = 0: massive solution versus conformal scaling. Phys. Rev. D 81, 016005 (2010)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Instituto de Física, UFF–Universidade Federal Fluminense, Campus da Praia Vermelha, Avenida General Milton Tavares de Souza s/n, 24210-346, Niterói, RJ, Brazil

    R. F. Sobreiro & A. A. Tomaz

  2. IFSEMG–Instituto Federal de Educação, Ciência e Tecnologia, Rua Bernardo Mascarenhas 1283, 36080-001, Juiz de Fora, MG, Brazil

    V. J. Vasquez Otoya

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  1. R. F. Sobreiro
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  2. A. A. Tomaz
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  3. V. J. Vasquez Otoya
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Correspondence to R. F. Sobreiro.

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Sobreiro, R.F., Tomaz, A.A. & Vasquez Otoya, V.J. de Sitter gauge theories and induced gravities. Eur. Phys. J. C 72, 1991 (2012). https://doi.org/10.1140/epjc/s10052-012-1991-4

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  • DOI: https://doi.org/10.1140/epjc/s10052-012-1991-4

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