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Non-local Effects of Conformal Anomaly

  • Krzysztof A. Meissner
  • Hermann Nicolai
Article
  • 26 Downloads
Part of the following topical collections:
  1. Black holes, Gravitational waves and Space Time Singularities

Abstract

It is shown that the nonlocal anomalous effective actions corresponding to the quantum breaking of the conformal symmetry can lead to observable modifications of Einstein’s equations. The fact that Einstein’s general relativity is in perfect agreement with all observations including cosmological or recently observed gravitational waves imposes strong restrictions on the field content of possible extensions of Einstein’s theory: all viable theories should have vanishing conformal anomalies. It is shown that a complete cancellation of conformal anomalies in \(D=4\) for both the \(C^2\) invariant and the Euler (Gauss–Bonnet) invariant can only be achieved for N-extended supergravity multiplets with \(N \ge 5\).

Keywords

Conformal anomaly Extended supergravities 

Notes

Acknowledgements

K.A.M. would like to thank the AEI for hospitality and support during this work; he was also partially supported by the Polish National Science Centre Grant DEC-2017/25/B/ST2/00165. H.N. would like to thank S. Kuzenko and P. Bouwknegt for hospitality at UWA in Perth and ANU in Canberra, respectively, while this work was underway, and A. Buonanno, M.J. Duff, J. Erdmenger, H. Godazgar, R. Kallosh, H. Osborn, A. Tseytlin and A. Schwimmer for discussions or correspondence. K.A.M. would like to thank R. Penrose for discussions in Czerwińsk and Oxford.

References

  1. 1.
    Meissner, K.A., Nicolai, H.: Conformal anomalies and gravitational waves. Phys. Lett. B 772, 169 (2017)ADSCrossRefzbMATHGoogle Scholar
  2. 2.
    Meissner, K.A., Nicolai, H.: Conformal anomaly and off-shell extensions of gravity. Phys. Rev. D 96, 041701 (2017)ADSCrossRefGoogle Scholar
  3. 3.
    Godazgar, H., Meissner, K.A., Nicolai, H.: Conformal anomalies and the Einstein field equations. JHEP 1(704), 165 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Deser, S., Duff, M.J., Isham, C.: Nonlocal conformal anomalies. Nucl. Phys. B 111, 45 (1976)ADSCrossRefzbMATHGoogle Scholar
  5. 5.
    Duff, M.J.: Observations on conformal anomalies. Nucl. Phys. B 125, 334 (1977)ADSCrossRefGoogle Scholar
  6. 6.
    Christensen, S.M., Duff, M.J.: Axial and conformal anomalies for arbitrary spin in gravity and supergravity. Phys. Lett. 76B, 571 (1978)ADSCrossRefGoogle Scholar
  7. 7.
    Christensen, S.M., Duff, M.J.: New gravitational index theorems and supertheorems. Nucl. Phys. B 154, 301 (1979)ADSCrossRefzbMATHGoogle Scholar
  8. 8.
    Fradkin, E., Tseytlin, A.: One loop beta function in conformal supergravities. Nucl. Phys. B 203, 157 (1982)ADSCrossRefGoogle Scholar
  9. 9.
    Fradkin, E., Tseytlin, A.: Off-shell one loop divergences in Gauged O(N) supergravities. Phys. Lett. B 117, 303 (1982)ADSCrossRefGoogle Scholar
  10. 10.
    Fradkin, E., Tseytlin, A.: Instanton zero modes and beta functions in supergravities. Phys. Lett. B 134, 187 (1984)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Deser, S., Schwimmer, A.: Geometric classification of conformal anomalies in arbitrary dimensions. Phys. Lett. B 309, 279 (1993)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Erdmenger, J., Osborn, H.: Conserved currents and the energy momentum tensor in conformally invariant theories for general dimensions. Nucl. Phys. B 483, 431 (1997)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Deser, S.: Conformal anomalies: recent progress Helv. Phys. Acta 69, 570 (1996)zbMATHGoogle Scholar
  14. 14.
    Polyakov, A.M.: Quantum geometry of bosonic strings. Phys. Lett. B 103, 207 (1981)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Distler, J., Kawai, H.: Conformal field theory and 2D quantum gravity. Nucl. Phys. B 321, 509 (1989)ADSCrossRefGoogle Scholar
  16. 16.
    Meissner, K.A., Nicolai, H.: Conformal symmetry and the standard model. Phys. Lett. B 648, 312 (2007)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Latosiński, A., Lewandowski, A., Meissner, K.A., Nicolai, H.: Conformal standard model with an extended scalar sector. JHEP 1510, 170 (2015)ADSCrossRefGoogle Scholar
  18. 18.
    Davies, P.C.W.: Singularity avoidance and quantum conformal anomalies. Phys. Lett. B 68, 402 (1977)ADSCrossRefGoogle Scholar
  19. 19.
    Fischetti, M.V., Hartle, J.B., Hu, B.L.: Quantum effects in the early universe. Phys. Rev. D 20, 1757 (1979)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Mazur, P.O., Mottola, E.: Weyl cohomology and the effective action for conformal anomalies. Phys. Rev. D 64, 104022 (2001)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Trautman, A.: Radiation and boundary conditions in the theory of gravitation. Bull. Acad. Polon. Sci. 6, 407 (1958)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Riegert, R.J.: A nonlocal action for the trace anomaly. Phys. Lett. B 134, 56 (1984)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Barvinsky, A.O., Gusev, Y.V., Vilkovisky, G.A., Zhytnikov, V.V.: The one loop effective action and trace anomaly in four-dimensions. Nucl. Phys. B439, 561 (1995)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Osborn, H., Petkou, A.C.: Implications of conformal invariance in field theories for general dimensions. Ann. Phys. 231, 311 (1994)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Schwimmer, A., Theisen, S.: Spontaneous breaking of conformal invariance and trace anomaly matching. Nucl. Phys. B 847, 590 (2011)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Komargodski, Z., Schwimmer, A.: On renormalization group flows in four dimensions. JHEP 1112, 099 (2011)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Mottola, E.: Scalar gravitational waves in the effective theory of gravity. JHEP 1707, 043 (2017). Erratum: JHEP 1709 (2017) 107Google Scholar
  28. 28.
    Erdmenger, J.: Conformally covariant differential operators: properties and applications. Class. Quant. Grav. 14, 2061 (1997)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Waylen, P.C.: Gravitational waves in an expanding universe. Proc. R. Soc. Lond. A362, 245 (1978)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Mukhanov, V.: Physical Foundations of Cosmology. Cambridge University Press, Cambridge (2005)CrossRefzbMATHGoogle Scholar
  31. 31.
    Tseytlin, A.: On partition function and Weyl anomaly of conformal higher spin fields. Nucl. Phys. B 877, 598 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Parker, L.: Recent Developments in Gravitation, Cargèse. Springer, New York (1978)Google Scholar
  33. 33.
    Eguchi, T., Gilkey, P.B., Hanson, A.J.: Gravitation, gauge theories and differential geometry. Phys. Rep. 66, 213 (1980)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    Birrell, N.D., Davies, P.C.W.: Quantum Fields in Curved Space. Cambridge University Press, Cambridge (1982)CrossRefzbMATHGoogle Scholar
  35. 35.
    Vassilevich, D.: Heat kernel expansion: user’s manual. Phys. Rep. 388, 279 (2003)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Bastianelli, F., van Nieuwenhuizen, P.: Path Integrals and Anomalies in Curved Space. Cambridge University Press, Cambridge (2009)zbMATHGoogle Scholar
  37. 37.
    Larsen, F., Lisbao, P.: Divergences and boundary modes in N = 8 supergravity. JHEP 1601, 024 (2016)ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    Nicolai, H., Townsend, P.K.: N = 3 supersymmetry multiplets with vanishing trace anomaly: building blocks of the N \(>\) 3 supergravities. Phys. Lett. B 98, 257 (1981)ADSCrossRefGoogle Scholar
  39. 39.
    Christensen, S.M., Duff, M.J., Gibbons, G.W., Rocek, M.: Vanishing one loop beta function in Gauged N \(>\) 4 supergravity. Phys. Rev. Lett. 45, 161 (1980)ADSCrossRefGoogle Scholar
  40. 40.
    Curtright, T.: Charge renormalization and high spin fields. Phys. Lett. B 102, 17 (1981)ADSCrossRefGoogle Scholar
  41. 41.
    Gibbons, G.W., Nicolai, H.: One loop effects on the round seven sphere. Phys. Lett. 143B, 108 (1984)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    Inami, T., Yamagishi, K.: Vanishing quantum vacuum energy in eleven-dimensional supergravity on the round seven sphere. Phys. Lett. B 143, 115 (1984)ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    Butter, D., Ciceri, F., de Wit, B., Sahoo, B.: Construction of all N = 4 conformal supergravities. Phys. Rev. Lett. 118, 081602 (2017)ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    de Wit, B., Ferrara, S.: On higher order invariants in extended supergravity. Phys. Lett. B 81, 317 (1979)ADSCrossRefGoogle Scholar
  45. 45.
    Günaydin, M., Marcus, N.: The unitary supermultiplet of N = 8 conformal superalgebra involving fields of spin 2. Class. Quant. Grav. 2, L19 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Julia, B., Nicolai, H.: Conformal internal symmetry of 2-d sigma models coupled to gravity and a dilaton. Nucl. Phys. B 482, 431 (1996)ADSCrossRefzbMATHGoogle Scholar
  47. 47.
    Hull, C.M.: Symmetries and compactifications of (4,0) conformal gravity. JHEP 0012, 007 (2000)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  48. 48.
    West, P.C.: E(11) and M theory. Class. Quant. Grav. 18, 4443 (2001)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    Meissner, K.A., Nicolai, H.: Standard model fermions and N = 8 supergravity. Phys. Rev. D 91, 065029 (2015)ADSMathSciNetCrossRefGoogle Scholar
  50. 50.
    Hooft, G.T.: Local conformal symmetry: the missing symmetry component for space and time. Int. J. Mod. Phys. D 24, 1543001 (2015)ADSCrossRefzbMATHGoogle Scholar
  51. 51.
    Marcus, N.: Composite anomalies in supergravity. Phys. Lett. B 157, 383 (1985)ADSMathSciNetCrossRefGoogle Scholar
  52. 52.
    Carrasco, J.J.M., Kallosh, R., Roiban, R., Tseytlin, A.A.: On the U(1) duality anomaly and the S-matrix of N = 4 supergravity. JHEP 1307, 029 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  53. 53.
    Bern, Z., Davies, S., Dennen, T.: Enhanced ultraviolet cancellations in N = 5 supergravity at four loops. Phys. Rev. D 90, 105011 (2014)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of PhysicsUniversity of WarsawWarsawPoland
  2. 2.Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)PotsdamGermany

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