- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Minimal models of field theories: Chiral higher spin gravity

Evgeny Skvortsov1,2,* and Richard Van Dongen1

  • 1Service de Physique de l’Univers, Champs et Gravitation, Université de Mons, 20 place du Parc, 7000 Mons, Belgium
  • 2Lebedev Institute of Physics, Leninsky Avenue 53, 119991 Moscow, Russia

  • *Research Associate of the Fund for Scientific Research-FNRS, Belgium.
PDF

Phys. Rev. D 106, 045006 – Published 5 August, 2022

DOI: https://doi.org/10.1103/PhysRevD.106.045006

Abstract

There exists a unique class of local higher spin gravities with propagating massless fields in 4d—chiral higher spin gravity. Originally, it was formulated in the light-cone gauge. We construct a covariant form of this theory as a free differential algebra up to the next-to-leading order, i.e., at the level of equations of motion. It also contains the recently discovered covariant forms of the higher spin extensions of self-dual Yang-Mills and self-dual gravity, as well as self-dual Yang-Mills and self-dual gravity themselves. From the mathematical viewpoint the result is equivalent to taking the minimal model (in the sense of L∞-algebras) of the jet-space extension of the BV-BRST formulation of chiral higher spin gravity, thereby, containing also information about (presymplectic AKSZ) action, counterterms, anomalies, etc.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (91)

  1. M. Blencowe, A consistent interacting massless higher spin field theory in D=(2+1), Classical Quantum Gravity 6, 443 (1989).
  2. E. Bergshoeff, M. P. Blencowe, and K. S. Stelle, Area preserving diffeomorphisms and higher spin algebra, Commun. Math. Phys. 128, 213 (1990).
  3. A. Campoleoni, S. Fredenhagen, S. Pfenninger, and S. Theisen, Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields, J. High Energy Phys. 11 (2010) 007.
  4. M. Henneaux and S.-J. Rey, Nonlinear W∞ as asymptotic symmetry of three-dimensional higher spin anti–de Sitter gravity, J. High Energy Phys. 12 (2010) 007.
  5. C. N. Pope and P. K. Townsend, Conformal higher spin in (2+1)-dimensions, Phys. Lett. B 225, 245 (1989).
  6. E. S. Fradkin and V. Ya. Linetsky, A superconformal theory of massless higher spin fields in D=(2+1), Mod. Phys. Lett. A 04, 731 (1989); Ann. Phys. (N.Y.) 198, 293 (1990).
  7. M. Grigoriev, I. Lovrekovic, and E. Skvortsov, New conformal higher spin gravities in 3d, J. High Energy Phys. 01 (2020) 059.
  8. A. Y. Segal, Conformal higher spin theory, Nucl. Phys. B664, 59 (2003).
  9. A. A. Tseytlin, On limits of superstring in AdS5×S5, Teor. Mat. Fiz. 133, 69 (2002) [Theor. Math. Phys. 133, 1376 (2002)].
  10. X. Bekaert, E. Joung, and J. Mourad, Effective action in a higher-spin background, J. High Energy Phys. 02 (2011) 048.
  11. R. R. Metsaev, Poincare invariant dynamics of massless higher spins: Fourth order analysis on mass shell, Mod. Phys. Lett. A 06, 359 (1991).
  12. R. R. Metsaev, S matrix approach to massless higher spins theory. 2: The Case of internal symmetry, Mod. Phys. Lett. A 06, 2411 (1991).
  13. D. Ponomarev and E. D. Skvortsov, Light-front higher-spin theories in flat space, J. Phys. A 50, 095401 (2017).
  14. E. D. Skvortsov, T. Tran, and M. Tsulaia, Quantum Chiral Higher Spin Gravity, Phys. Rev. Lett. 121, 031601 (2018).
  15. E. Skvortsov, T. Tran, and M. Tsulaia, More on quantum chiral higher spin gravity, Phys. Rev. D 101, 106001 (2020).
  16. D. Ponomarev, Chiral higher spin theories and self-duality, J. High Energy Phys. 12 (2017) 141.
  17. K. Krasnov, E. Skvortsov, and T. Tran, Actions for self-dual higher spin gravities, J. High Energy Phys. 08 (2021) 076.
  18. R. de Mello Koch, A. Jevicki, K. Suzuki, and J. Yoon, AdS maps and diagrams of bi-local holography, J. High Energy Phys. 03 (2019) 133.
  19. O. Aharony, S. M. Chester, and E. Y. Urbach, A derivation of AdS/CFT for vector models, J. High Energy Phys. 03 (2021) 208.
  20. M. Sperling and H. C. Steinacker, Covariant 4-dimensional fuzzy spheres, matrix models and higher spin, J. Phys. A 50, 375202 (2017).
  21. T. Tran, Twistor constructions for higher-spin extensions of (self-dual) Yang-Mills, J. High Energy Phys. 11 (2021) 117.
  22. H. Steinacker and T. Tran, A twistorial description of the IKKT-matrix model, arXiv:2203.05436.
  23. G. Chalmers and W. Siegel, Simplifying algebra in Feynman graphs. Part 2. Spinor helicity from the space-cone, Phys. Rev. D 59, 045013 (1999).
  24. D. Chakrabarti, J. Qiu, and C. B. Thorn, Scattering of glue by glue on the light-cone worldsheet. I. Helicity non-conserving amplitudes, Phys. Rev. D 72, 065022 (2005).
  25. D. Chakrabarti, J. Qiu, and C. B. Thorn, Scattering of glue by glue on the light-cone worldsheet. II. Helicity conserving amplitudes, Phys. Rev. D 74, 045018 (2006); 76, 089901(E) (2007).
  26. A. K. H. Bengtsson, Notes on cubic and quartic light-front kinematics, arXiv:1604.01974.
  27. D. Ponomarev, Off-shell spinor-helicity amplitudes from light-cone deformation procedure, J. High Energy Phys. 12 (2016) 117.
  28. A. K. H. Bengtsson, I. Bengtsson, and N. Linden, Interacting higher spin gauge fields on the light front, Classical Quantum Gravity 4, 1333 (1987).
  29. P. Benincasa and E. Conde, Exploring the S-matrix of massless particles, Phys. Rev. D 86, 025007 (2012).
  30. M. H. Goroff and A. Sagnotti, The ultraviolet behavior of Einstein gravity, Nucl. Phys. B266, 709 (1986).
  31. R. R. Metsaev and A. A. Tseytlin, Curvature cubed terms in string theory effective actions, Phys. Lett. B 185, 52 (1987).
  32. E. Skvortsov and T. Tran, One-loop finiteness of chiral higher spin gravity, J. High Energy Phys. 07 (2020) 021.
  33. E. S. Fradkin and A. A. Tseytlin, Quantum properties of higher dimensional and dimensionally reduced supersymmetric theories, Nucl. Phys. B227, 252 (1983).
  34. R. Gopakumar, R. K. Gupta, and S. Lal, The heat kernel on AdS, J. High Energy Phys. 11 (2011) 010.
  35. A. A. Tseytlin, On partition function and Weyl anomaly of conformal higher spin fields, Nucl. Phys. B877, 598 (2013).
  36. S. Giombi and I. R. Klebanov, One loop tests of higher spin AdS/CFT, J. High Energy Phys. 12 (2013) 068.
  37. S. Giombi, I. R. Klebanov, and A. A. Tseytlin, Partition functions and casimir energies in higher spin AdSd+1/CFTd, Phys. Rev. D 90, 024048 (2014).
  38. M. Beccaria, X. Bekaert, and A. A. Tseytlin, Partition function of free conformal higher spin theory, J. High Energy Phys. 08 (2014) 113.
  39. M. Beccaria and A. A. Tseytlin, Higher spins in AdS5 at one loop: Vacuum energy, boundary conformal anomalies and AdS/CFT, J. High Energy Phys. 11 (2014) 114.
  40. M. Beccaria and A. A. Tseytlin, On higher spin partition functions, J. Phys. A 48, 275401 (2015).
  41. M. Günaydin, E. D. Skvortsov, and T. Tran, Exceptional F(4) higher-spin theory in AdS6 at one-loop and other tests of duality, J. High Energy Phys. 11 (2016) 168.
  42. J.-B. Bae, E. Joung, and S. Lal, One-loop test of free SU(N) adjoint model holography, J. High Energy Phys. 04 (2016) 061.
  43. E. D. Skvortsov and T. Tran, AdS/CFT in fractional dimension and higher spin gravity at one loop, Universe 3, 61 (2017).
  44. E. Conde, E. Joung, and K. Mkrtchyan, Spinor-helicity three-point amplitudes from local cubic interactions, J. High Energy Phys. 08 (2016) 040.
  45. M. F. Atiyah, Geometry of Yang-Mills Fields (Scuola Normale Superiore, Pisa, 1979).
  46. N. J. Hitchin, Linear field equations on selfdual spaces, Proc. R Soc. A 370, 173 (1980).
  47. M. G. Eastwood, R. Penrose, and R. O. Wells, Cohomology and massless fields, Commun. Math. Phys. 78, 305 (1981).
  48. N. M. J. Woodhouse, Real methods in twistor theory, Classical Quantum Gravity 2, 257 (1985).
  49. D. Sullivan, Infinitesimal computations in topology, Publ. Math. IHES 47, 269 (1977).
  50. G. Barnich and M. Grigoriev, A Poincare lemma for sigma models of AKSZ type, J. Geom. Phys. 61, 663 (2011).
  51. M. Grigoriev and A. Kotov, Gauge PDE and AKSZ-type sigma models, Fortschr. Phys. 67, 1910007 (2019).
  52. K. Krasnov and E. Skvortsov, Flat self-dual gravity, J. High Energy Phys. 08 (2021) 082.
  53. F. Brandt, Gauge covariant algebras and local BRST cohomology, Contemp. Math. 219, 53 (1998).
  54. F. Brandt, Local BRST cohomology and covariance, Commun. Math. Phys. 190, 459 (1997).
  55. G. Barnich, F. Brandt, and M. Henneaux, Local BRST cohomology in the antifield formalism. 1. General theorems, Commun. Math. Phys. 174, 57 (1995).
  56. G. Barnich, F. Brandt, and M. Henneaux, Local BRST cohomology in the antifield formalism. II. Application to Yang-Mills theory, Commun. Math. Phys. 174, 93 (1995).
  57. G. Barnich and M. Grigoriev, First order parent formulation for generic gauge field theories, J. High Energy Phys. 01 (2011) 122.
  58. M. Grigoriev, Parent formulations, frame-like Lagrangians, and generalized auxiliary fields, J. High Energy Phys. 12 (2012) 048.
  59. M. Grigoriev, K. Mkrtchyan, and E. Skvortsov, Matter-free higher spin gravities in 3D: Partially-massless fields and general structure, Phys. Rev. D 102, 066003 (2020).
  60. P. van Nieuwenhuizen, Free graded differential superalgebras, in Group Theoretical Methods in Physics. Proceedings of the 11th International Colloquium, Istanbul, Turkey, 1982 (Springer-Verlag, Berlin, 1982), pp. 228–247.
  61. R. D’Auria, P. Fre, and T. Regge, Graded lie algebra cohomology and supergravity, Riv. Nuovo Cimento 3N12, 1 (1980).
  62. M. A. Vasiliev, Consistent equations for interacting massless fields of all spins in the first order in curvatures, Ann. Phys. (N.Y.) 190, 59 (1989).
  63. J. D. Stasheff, Homotopy associativity of H-spaces. I, Trans. Am. Math. Soc. 108, 275 (1963).
  64. M. Alexandrov, M. Kontsevich, A. Schwarz, and O. Zaboronsky, The geometry of the master equation and topological quantum field theory, Int. J. Mod. Phys. A 12, 1405 (1997).
  65. G. Barnich and M. Henneaux, Consistent couplings between fields with a gauge freedom and deformations of the master equation, Phys. Lett. B 311, 123 (1993).
  66. N. Boulanger, P. Kessel, E. D. Skvortsov, and M. Taronna, Higher spin interactions in four-dimensions: Vasiliev versus Fronsdal, J. Phys. A 49, 095402 (2016).
  67. E. D. Skvortsov and M. Taronna, On locality, holography and unfolding, J. High Energy Phys. 11 (2015) 044.
  68. R. Penrose, Zero rest mass fields including gravitation: Asymptotic behavior, Proc. R. Soc. A 284, 159 (1965).
  69. Advances in Twistor Theory, edited by L. P. Hughston, R. S. Ward, M. G. Eastwood, M. L. Ginsberg, A. P. Hodges, S. A. Huggett, T. R. Hurd, R. O. Jozsa, R. Penrose, A. Popovich et al. (Pitman Publishing Limited, London, 1979).
  70. A. Sharapov and E. Skvortsov, Higher spin gravities and presymplectic AKSZ models, Nucl. Phys. B972, 115551 (2021).
  71. M. A. Vasiliev, Free massless fields of arbitrary spin in the de Sitter space and initial data for a higher spin superalgebra, Fortschr. Phys. 35, 741 (1987).
  72. V. Didenko and E. Skvortsov, Elements of Vasiliev theory, arXiv:1401.2975.
  73. K. Krasnov, Self-dual gravity, Classical Quantum Gravity 34, 095001 (2017).
  74. T. Adamo, L. Mason, and A. Sharma, Celestial w1+∞ symmetries from twistor space, SIGMA 18, 016 (2022).
  75. W. Siegel, Selfdual N=8 supergravity as closed N=2 (N=4) strings, Phys. Rev. D 47, 2504 (1993).
  76. M. Abou-Zeid and C. M. Hull, A chiral perturbation expansion for gravity, J. High Energy Phys. 02 (2006) 057.
  77. E. Skvortsov and R. Van Dongen, Minimal models of field theories: SDYM and SDGR, arXiv:2204.09313.
  78. A. Sharapov and E. Skvortsov, A∞ algebras from slightly broken higher spin symmetries, J. High Energy Phys. 09 (2019) 024.
  79. A. Sharapov and E. Skvortsov, Formal higher spin gravities, Nucl. Phys. B941, 838 (2019).
  80. A. Sharapov and E. Skvortsov, Characteristic cohomology and observables in higher spin gravity, J. High Energy Phys. 12 (2020) 190.
  81. P. Gerasimenko, A. Sharapov, and E. Skvortsov, Slightly broken higher spin symmetry: General structure of correlators, J. High Energy Phys. 01 (2022) 097.
  82. A. A. Sharapov and E. D. Skvortsov, A simple construction of associative deformations, Lett. Math. Phys. 109, 623 (2019).
  83. A. Sharapov and E. Skvortsov, Integrable models from non-commutative geometry with applications to 3D dualities, in Proceedings of the 21st Hellenic School and Workshops on Elementary Particle Physics and Gravity (2022), arXiv:2204.08903.
  84. A. A. Sharapov and E. D. Skvortsov, Formal higher-spin theories and Kontsevich–Shoikhet–Tsygan formality, Nucl. Phys. B921, 538 (2017).
  85. C. Devchand and V. Ogievetsky, Interacting fields of arbitrary spin and N>4 supersymmetric selfdual Yang-Mills equations, Nucl. Phys. B481, 188 (1996).
  86. R. R. Metsaev, Cubic interaction vertices for N=1 arbitrary spin massless supermultiplets in flat space, J. High Energy Phys. 08 (2019) 130.
  87. R. R. Metsaev, Cubic interactions for arbitrary spin N-extended massless supermultiplets in 4d flat space, J. High Energy Phys. 11 (2019) 084.
  88. R. S. Ward, On Selfdual gauge fields, Phys. Lett. 61A, 81 (1977).
  89. R. Penrose, Nonlinear gravitons and curved twistor theory, Gen. Relativ. Gravit. 7, 31 (1976).
  90. M. F. Atiyah, N. J. Hitchin, V. G. Drinfeld, and Y. I. Manin, Construction of instantons, Phys. Lett. 65A, 185 (1978).
  91. M. A. Vasiliev, Higher spin gauge theories: Star-product and AdS space, arXiv:hep-th/9910096.

Outline

Information

Phys. Rev. D 106, 045006– Published 5 August, 2022
  • Received 5 June 2022
  • Accepted 25 July 2022
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation