Skip to main content

Non-local Effects of Conformal Anomaly

Foundations of Physics volume 48, pages 1150–1158 (2018)Cite this article

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 \(N \ge 5\).

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price includes VAT (USA)
Tax calculation will be finalised during checkout.

Notes

  1. We are grateful to M.J. Duff for correspondence on this point.

References

  1. Meissner, K.A., Nicolai, H.: Conformal anomalies and gravitational waves. Phys. Lett. B 772, 169 (2017)

    ADS  Article  Google Scholar 

  2. Meissner, K.A., Nicolai, H.: Conformal anomaly and off-shell extensions of gravity. Phys. Rev. D 96, 041701 (2017)

    ADS  Article  Google Scholar 

  3. Godazgar, H., Meissner, K.A., Nicolai, H.: Conformal anomalies and the Einstein field equations. JHEP 1(704), 165 (2017)

    MathSciNet  Article  Google Scholar 

  4. Deser, S., Duff, M.J., Isham, C.: Nonlocal conformal anomalies. Nucl. Phys. B 111, 45 (1976)

    ADS  Article  Google Scholar 

  5. Duff, M.J.: Observations on conformal anomalies. Nucl. Phys. B 125, 334 (1977)

    ADS  Article  Google Scholar 

  6. Christensen, S.M., Duff, M.J.: Axial and conformal anomalies for arbitrary spin in gravity and supergravity. Phys. Lett. 76B, 571 (1978)

    ADS  Article  Google Scholar 

  7. Christensen, S.M., Duff, M.J.: New gravitational index theorems and supertheorems. Nucl. Phys. B 154, 301 (1979)

    ADS  Article  Google Scholar 

  8. Fradkin, E., Tseytlin, A.: One loop beta function in conformal supergravities. Nucl. Phys. B 203, 157 (1982)

    ADS  Article  Google Scholar 

  9. Fradkin, E., Tseytlin, A.: Off-shell one loop divergences in Gauged O(N) supergravities. Phys. Lett. B 117, 303 (1982)

    ADS  Article  Google Scholar 

  10. Fradkin, E., Tseytlin, A.: Instanton zero modes and beta functions in supergravities. Phys. Lett. B 134, 187 (1984)

    ADS  MathSciNet  Article  Google Scholar 

  11. Deser, S., Schwimmer, A.: Geometric classification of conformal anomalies in arbitrary dimensions. Phys. Lett. B 309, 279 (1993)

    ADS  MathSciNet  Article  Google Scholar 

  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)

    ADS  MathSciNet  Article  Google Scholar 

  13. Deser, S.: Conformal anomalies: recent progress Helv. Phys. Acta 69, 570 (1996)

    MATH  Google Scholar 

  14. Polyakov, A.M.: Quantum geometry of bosonic strings. Phys. Lett. B 103, 207 (1981)

    ADS  MathSciNet  Article  Google Scholar 

  15. Distler, J., Kawai, H.: Conformal field theory and 2D quantum gravity. Nucl. Phys. B 321, 509 (1989)

    ADS  Article  Google Scholar 

  16. Meissner, K.A., Nicolai, H.: Conformal symmetry and the standard model. Phys. Lett. B 648, 312 (2007)

    ADS  MathSciNet  Article  Google Scholar 

  17. Latosiński, A., Lewandowski, A., Meissner, K.A., Nicolai, H.: Conformal standard model with an extended scalar sector. JHEP 1510, 170 (2015)

    ADS  Article  Google Scholar 

  18. Davies, P.C.W.: Singularity avoidance and quantum conformal anomalies. Phys. Lett. B 68, 402 (1977)

    ADS  Article  Google Scholar 

  19. Fischetti, M.V., Hartle, J.B., Hu, B.L.: Quantum effects in the early universe. Phys. Rev. D 20, 1757 (1979)

    ADS  MathSciNet  Article  Google Scholar 

  20. Mazur, P.O., Mottola, E.: Weyl cohomology and the effective action for conformal anomalies. Phys. Rev. D 64, 104022 (2001)

    ADS  MathSciNet  Article  Google Scholar 

  21. Trautman, A.: Radiation and boundary conditions in the theory of gravitation. Bull. Acad. Polon. Sci. 6, 407 (1958)

    MathSciNet  MATH  Google Scholar 

  22. Riegert, R.J.: A nonlocal action for the trace anomaly. Phys. Lett. B 134, 56 (1984)

    ADS  MathSciNet  Article  Google Scholar 

  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)

    ADS  MathSciNet  Article  Google Scholar 

  24. Osborn, H., Petkou, A.C.: Implications of conformal invariance in field theories for general dimensions. Ann. Phys. 231, 311 (1994)

    ADS  MathSciNet  Article  Google Scholar 

  25. Schwimmer, A., Theisen, S.: Spontaneous breaking of conformal invariance and trace anomaly matching. Nucl. Phys. B 847, 590 (2011)

    ADS  MathSciNet  Article  Google Scholar 

  26. Komargodski, Z., Schwimmer, A.: On renormalization group flows in four dimensions. JHEP 1112, 099 (2011)

    ADS  MathSciNet  Article  Google Scholar 

  27. Mottola, E.: Scalar gravitational waves in the effective theory of gravity. JHEP 1707, 043 (2017). Erratum: JHEP 1709 (2017) 107

  28. Erdmenger, J.: Conformally covariant differential operators: properties and applications. Class. Quant. Grav. 14, 2061 (1997)

    ADS  MathSciNet  Article  Google Scholar 

  29. Waylen, P.C.: Gravitational waves in an expanding universe. Proc. R. Soc. Lond. A362, 245 (1978)

    ADS  MathSciNet  Article  Google Scholar 

  30. Mukhanov, V.: Physical Foundations of Cosmology. Cambridge University Press, Cambridge (2005)

    Book  Google Scholar 

  31. Tseytlin, A.: On partition function and Weyl anomaly of conformal higher spin fields. Nucl. Phys. B 877, 598 (2013)

    ADS  MathSciNet  Article  Google Scholar 

  32. Parker, L.: Recent Developments in Gravitation, Cargèse. Springer, New York (1978)

    Google Scholar 

  33. Eguchi, T., Gilkey, P.B., Hanson, A.J.: Gravitation, gauge theories and differential geometry. Phys. Rep. 66, 213 (1980)

    ADS  MathSciNet  Article  Google Scholar 

  34. Birrell, N.D., Davies, P.C.W.: Quantum Fields in Curved Space. Cambridge University Press, Cambridge (1982)

    Book  Google Scholar 

  35. Vassilevich, D.: Heat kernel expansion: user’s manual. Phys. Rep. 388, 279 (2003)

    ADS  MathSciNet  Article  Google Scholar 

  36. Bastianelli, F., van Nieuwenhuizen, P.: Path Integrals and Anomalies in Curved Space. Cambridge University Press, Cambridge (2009)

    MATH  Google Scholar 

  37. Larsen, F., Lisbao, P.: Divergences and boundary modes in N = 8 supergravity. JHEP 1601, 024 (2016)

    ADS  MathSciNet  Article  Google Scholar 

  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)

    ADS  Article  Google Scholar 

  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)

    ADS  Article  Google Scholar 

  40. Curtright, T.: Charge renormalization and high spin fields. Phys. Lett. B 102, 17 (1981)

    ADS  Article  Google Scholar 

  41. Gibbons, G.W., Nicolai, H.: One loop effects on the round seven sphere. Phys. Lett. 143B, 108 (1984)

    ADS  MathSciNet  Article  Google Scholar 

  42. Inami, T., Yamagishi, K.: Vanishing quantum vacuum energy in eleven-dimensional supergravity on the round seven sphere. Phys. Lett. B 143, 115 (1984)

    ADS  MathSciNet  Article  Google Scholar 

  43. Butter, D., Ciceri, F., de Wit, B., Sahoo, B.: Construction of all N = 4 conformal supergravities. Phys. Rev. Lett. 118, 081602 (2017)

    ADS  MathSciNet  Article  Google Scholar 

  44. de Wit, B., Ferrara, S.: On higher order invariants in extended supergravity. Phys. Lett. B 81, 317 (1979)

    ADS  Article  Google Scholar 

  45. Günaydin, M., Marcus, N.: The unitary supermultiplet of N = 8 conformal superalgebra involving fields of spin 2. Class. Quant. Grav. 2, L19 (1985)

    ADS  MathSciNet  Article  Google Scholar 

  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)

    ADS  Article  Google Scholar 

  47. Hull, C.M.: Symmetries and compactifications of (4,0) conformal gravity. JHEP 0012, 007 (2000)

    ADS  MathSciNet  Article  Google Scholar 

  48. West, P.C.: E(11) and M theory. Class. Quant. Grav. 18, 4443 (2001)

    ADS  MathSciNet  Article  Google Scholar 

  49. Meissner, K.A., Nicolai, H.: Standard model fermions and N = 8 supergravity. Phys. Rev. D 91, 065029 (2015)

    ADS  MathSciNet  Article  Google Scholar 

  50. Hooft, G.T.: Local conformal symmetry: the missing symmetry component for space and time. Int. J. Mod. Phys. D 24, 1543001 (2015)

    ADS  Article  Google Scholar 

  51. Marcus, N.: Composite anomalies in supergravity. Phys. Lett. B 157, 383 (1985)

    ADS  MathSciNet  Article  Google Scholar 

  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)

    ADS  MathSciNet  Article  Google Scholar 

  53. Bern, Z., Davies, S., Dennen, T.: Enhanced ultraviolet cancellations in N = 5 supergravity at four loops. Phys. Rev. D 90, 105011 (2014)

    ADS  Article  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, Poland

    Krzysztof A. Meissner

  2. Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Mühlenberg 1, 14476, Potsdam, Germany

    Hermann Nicolai

Authors
  1. Krzysztof A. Meissner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hermann Nicolai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Krzysztof A. Meissner.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Meissner, K.A., Nicolai, H. Non-local Effects of Conformal Anomaly. Found Phys 48, 1150–1158 (2018). https://doi.org/10.1007/s10701-018-0160-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-018-0160-5

Keywords

  • Conformal anomaly
  • Extended supergravities