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Non-local Effects of Conformal Anomaly

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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 \(N \ge 5\).

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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)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  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)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  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)

    Article  ADS  MathSciNet  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)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  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)

    Article  ADS  MathSciNet  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)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  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)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  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)

    Article  ADS  MathSciNet  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)

    Article  ADS  MathSciNet  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)

    Article  ADS  MathSciNet  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)

    Article  ADS  MathSciNet  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)

    Article  ADS  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)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  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)

    Article  ADS  MathSciNet  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)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  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)

    Article  ADS  MathSciNet  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)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  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)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  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)

    Article  ADS  MathSciNet  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)

    Article  ADS  Google Scholar 

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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.

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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

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  1. Krzysztof A. Meissner
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Correspondence to Krzysztof A. Meissner.

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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

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