Journal of High Energy Physics

, 2019:124 | Cite as

One-loop quantum gravity from the N particle 4 spinning

  • Fiorenzo Bastianelli
  • Roberto BonezziEmail author
  • Olindo Corradini
  • Emanuele Latini
Open Access
Regular Article - Theoretical Physics


We construct a spinning particle that reproduces the propagation of the graviton on those curved backgrounds which solve the Einstein equations, with or without cosmological constant, i.e. Einstein manifolds. It is obtained by modifying the \( \mathcal{N} \) = 4 supersymmetric spinning particle by relaxing the gauging of the full SO(4) R-symmetry group to a parabolic subgroup, and selecting suitable Chern-Simons couplings on the worldline. We test it by computing the correct one-loop divergencies of quantum gravity in D = 4.


ERST Quantization Models of Quantum Gravity Sigma Models 


Open Access

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  1. [1]
    R. Bonezzi, A. Meyer and I. Sachs, Einstein gravity from the N = 4 spinning particle, JHEP10 (2018) 025 [arXiv:1807.07989] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    F.A. Berezin and M.S. Marinov, Particle spin dynamics as the Grassmann variant of classical mechanics, Annals Phys.104 (1977) 336 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    V.D. Gershun and V.I. Tkach, Classical and quantum dynamics of particles with arbitrary spin, JETP Lett.29 (1979) 288 [Pisma Zh. Eksp. Tear. Fiz.29 (1979) 320] [INSPIRE].
  4. [4]
    P.S. Howe, S. Penati, M. Pernici and P.K. Townsend, Wave equations for arbitrary spin from quantization of the extended supersymmetric spinning particle, Phys. Lett.B 215 (1988) 555 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    W. Siegel, Conformal invariance of extend ed spinning particl e mechanics, Int. J. Mod. Phys.A 3 (1988) 2713 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    W. Siegel, All free conformal representations in all dimensions, Int. J. Mod. Phys.A 4 (1989) 2015 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    S.M. Kuzenko and Z.V. Yarevskaya, Conformal invariance, N extended supersymmetry and massless spinning particles in anti-de Sitter space, Mod. Phys. Lett.A 11 (1996) 1653 [hep-th/9512115] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    F. Bastianelli, O. Corradini and E. Latini, Spinning particles and higher spin fields on (A)dS backgrounds, JHEP11 (2008) 054 [arXiv:0810.0188] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    O. Corradini, Half-integer higher spin fields in ( A)dS from spinning particle models, JHEP09 (2010) 113 [arXiv:1006.4452] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    F. Bastianelli and R. Bonezzi, One-loop quantum gravity from a worldline viewpoint, JHEP07 (2013) 016 [arXiv:1304.7135] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    P. Dai, Y.-T. Huang and W. Siegel, Worldgraph approach to Yang-Mills amplitudes from N = 2 spinning particle, JHEP10 (2008) 027 [arXiv:0807.0391] [INSPIRE].
  12. [12]
    X. Bekaert, N. Boulanger and S. Cnockaert, No self-interaction for two-column massless fields, J. Math. Phys.46 (2005) 012303 [hep-th/0407102] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    F. Bastianelli, O. Corradini and E. Latini, Higher spin fields from a worldline perspective, JHEP02 (2007) 072 [hep-th/0701055] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    G. ‘t Hooft and M.J.G. Veltman, One loop divergencies in the theory of gravitation, Ann. Inst. H. Poincare Phys. Theor.A 20 (1974) 69 [INSPIRE].
  15. [15]
    S.M. Christensen and M.J. Duff, Quantizing gravity with a cosmological constant, Nucl. Phys.B 170 (1980) 480 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    P.S. Howe, S. Penati, M. Pernici and P.K. Townsend, A particle mechanics description of antisymmetric tensor fields, Class. Quant. Grav.6 (1989) 1125 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    F. Bastianelli, P. Benincasa and S. Giombi, Worldline approach to vector and antisymmetric tensor fields, JHEP04 (2005) 010 [hep-th/0503155] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    W. Siegel, Relation between Eatalin- Vilkovisky and first quantized style ERST, Int. J. Mod. Phys.A 4 (1989) 3705 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    G. Barnich and M. Grigoriev, Hamiltonian ERST and Eatalin- Vilkovisky formalisms for second quantization of gauge theories, Commun. Math. Phys.254 (2005) 581 [hep-th/0310083] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    G. Barnich, M. Grigoriev, A. Semikhatov and I. Tipunin, Parent field theory and unfolding in ERST first-quantized terms, Commun. Math. Phys.260 (2005) 147 [hep-th/0406192] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    G. Barnich and M. Grigoriev, Parent form for higher spin fields on anti-de Sitter space, JHEP08 (2006) 013 [hep-th/0602166] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    F. Bastianelli, R. Bonezzi, O. Corradini and E. Latini, Effective action for higher spin fields on (A)dS backgrounds, JHEP12 (2012) 113 [arXiv:1210.4649] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    F. Bastianelli and P. van Nieuwenhuizen, Path integrals and anomalies in curved space, Cambridge University Press, Cambridge, U.K. (2006) [INSPIRE].CrossRefGoogle Scholar
  24. [24]
    F. Bastianelli, R. Bonezzi, O. Corradini and E. Latini, Extended SUSY quantum mechanics: transition amplitud es and path integrals, JHEP06 (2011) 023 [arXiv:1103.3993] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    F. Bastianelli, O. Corradini and A. Waldron, Detours and paths: ERST complexes and world line formalism, JHEP05 (2009) 017 [arXiv:0902.0530] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    F. Bastianelli and R. Bonezzi, Quantum theory of massless (p,0)-forms, JHEP09 (2011) 018 [arXiv:1107.3661] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    F. Bastianelli, R. Bonezzi and C. Iazeolla, Quantum theories of (p, q)-forms, JHEP08 (2012) 045 [arXiv:1204.5954] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    R. Bonezzi, O. Corradini, S.A. Franchino Vinas and P.A.G. Pisani, Worldline approach to noncommutative field theory, J. Phys.A 45 (2012) 405401 [arXiv:1204.1013] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  29. [29]
    R. Bonezzi, A. Meyer and I. Sachs, to appear.Google Scholar
  30. [30]
    C. Aragone and S. Deser, Consistency problems of hypergravity, Phys. Lett.B 86 (1979) 161 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  31. [31]
    E.S. Fradkin and M.A. Vasiliev, On the gravitational interaction of massless higher spin fields, Phys. Lett.B 189 (1987) 89 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Dipartimemo di Fisica e AstroromiaUniversità di BoloqnaBolognaItaly
  2. 2.INFNBolognaItaly
  3. 3.Max-Planck-Institut für GravitationphysikAlberl-Einstein-InstitutGolmGermany
  4. 4.Institute for PhysicsHumboldt University BerlinBerlinGermany
  5. 5.Dipartimento di Scienze Fisiche, Informatiche e MatematicheUniversità degli Studi di Modena e Reggio EmiliaModenaItaly
  6. 6.Dipartimemo di MatematicaUniversità di BolognaBolognaItaly

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