Advertisement

Journal of High Energy Physics

, 2017:63 | Cite as

From Diophantus to supergravity and massless higher spin multiplets

  • S. James GatesJr.
  • Konstantinos Koutrolikos
Open Access
Regular Article - Theoretical Physics

Abstract

We present a new method of deriving the off-shell spectrum of supergravity and massless 4D, \( \mathcal{N} \) = 1 higher spin multiplets without the need of an action and based on a set of natural requirements: (a.) existence of an underlying superspace description, (b.) an economical description of free, massless, higher spins and (c.) equal numbers of bosonic and fermionic degrees of freedom. We prove that for any theory that respects the above, the fermionic auxiliary components come in pairs and are gauge invariant and there are two types of bosonic auxiliary components. Type (1) are pairs of a (2, 0)-tensor with real or imaginary (1, 1)-tensor with non-trivial gauge transformations. Type (2) are singlets and gauge invariant. The outcome is a set of Diophantine equations, the solutions of which determine the off-shell spectrum of supergravity and massless higher spin multiplets. This approach provides (i ) a classification of the irreducible, supersymmetric, representations of arbitrary spin and (ii ) a very clean and intuitive explanation to why some of these theories have more than one formulations (e.g. the supergravity multiplet) and others do not.

Keywords

Supergravity Models Superspaces Supersymmetric Effective Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    S.M. Kuzenko, A.G. Sibiryakov and V.V. Postnikov, Massless gauge superfields of higher half integer superspins, JETP Lett. 57 (1993) 534 [INSPIRE].ADSGoogle Scholar
  2. [2]
    S.M. Kuzenko and A.G. Sibiryakov, Massless gauge superfields of higher integer superspins, JETP Lett. 57 (1993) 539 [INSPIRE].ADSGoogle Scholar
  3. [3]
    S.J. Gates Jr. and K. Koutrolikos, On 4D, \( \mathcal{N} \) = 1 massless gauge superfields of arbitrary superhelicity, JHEP 06 (2014) 098 [arXiv:1310.7385] [arXiv:1310.7386] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    S.J. Gates Jr. and K. Koutrolikos, A dynamical theory for linearized massive superspin 3/2, JHEP 03 (2014) 030 [arXiv:1310.7387] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    S.J. Gates Jr., S.M. Kuzenko and G. Tartaglino-Mazzucchelli, New massive supergravity multiplets, JHEP 02 (2007) 052 [hep-th/0610333] [INSPIRE].ADSCrossRefMATHMathSciNetGoogle Scholar
  6. [6]
    C. Fronsdal, Massless Fields with Integer Spin, Phys. Rev. D 18 (1978) 3624 [INSPIRE].ADSGoogle Scholar
  7. [7]
    J. Fang and C. Fronsdal, Massless Fields with Half Integral Spin, Phys. Rev. D 18 (1978) 3630 [INSPIRE].ADSGoogle Scholar
  8. [8]
    L.P.S. Singh and C.R. Hagen, Lagrangian formulation for arbitrary spin. 2. The fermion case, Phys. Rev. D 9 (1974) 910 [INSPIRE].
  9. [9]
    L.P.S. Singh and C.R. Hagen, Lagrangian formulation for arbitrary spin. 1. The boson case, Phys. Rev. D 9 (1974) 898 [INSPIRE].
  10. [10]
    P.S. Howe, K.S. Stelle and P.K. Townsend, The Relaxed Hypermultiplet: An Unconstrained N = 2 Superfield Theory, Nucl. Phys. B 214 (1983) 519 [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    C.F. Doran, M.G. Faux, S.J. Gates Jr., T. Hubsch, K.M. Iga and G.D. Landweber, On the matter of N = 2 matter, Phys. Lett. B 659 (2008) 441 [arXiv:0710.5245] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  12. [12]
    M. Faux, The Conformal Hyperplet, Int. J. Mod. Phys. A 32 (2017) 1750079 [arXiv:1610.07822] [INSPIRE].ADSCrossRefMATHMathSciNetGoogle Scholar
  13. [13]
    B.B. Deo and S.J. Gates Jr., Comments on nonminimal N = 1 scalar multiplets, Nucl. Phys. B 254 (1985) 187 [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    W. Siegel, Manifest Lorentz Invariance Sometimes Requires Nonlinearity, Nucl. Phys. B 238 (1984) 307 [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    V. Ogievetsky and E. Sokatchev, On Vector Superfield Generated by Supercurrent, Nucl. Phys. B 124 (1977) 309 [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    V.I. Ogievetsky and E.S. Sokatchev, The Axial Superfield and the Supergravity Group, Yad. Fiz. 28 (1978) 1631 [INSPIRE].Google Scholar
  17. [17]
    W. Siegel and S.J. Gates Jr., Superfield Supergravity, Nucl. Phys. B 147 (1979) 77 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  18. [18]
    B. de Wit and J.W. van Holten, Multiplets of Linearized SO(2) Supergravity, Nucl. Phys. B 155 (1979) 530 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  19. [19]
    S.J. Gates Jr. and W. Siegel, (3/2, 1) Superfield of O(2) Supergravity, Nucl. Phys. B 164 (1980) 484 [INSPIRE].
  20. [20]
    S. Deser, P.K. Townsend and W. Siegel, Higher Rank Representations of Lower Spin, Nucl. Phys. B 184 (1981) 333 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  21. [21]
    S.J. Gates Jr. and W. Siegel, Variant superfield representations, Nucl. Phys. B 187 (1981) 389 [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    V.I. Ogievetsky and E. Sokatchev, On Gauge Spinor Superfield, JETP Lett. 23 (1976) 58 [INSPIRE].ADSGoogle Scholar
  23. [23]
    M. Faux and S.J. Gates Jr., Adinkras: A Graphical technology for supersymmetric representation theory, Phys. Rev. D 71 (2005) 065002 [hep-th/0408004] [INSPIRE].ADSGoogle Scholar
  24. [24]
    M. Calkins, D.E.A. Gates, S.J. Gates Jr. and W.M. Golding, Think Different: Applying the Old Macintosh Mantra to the Computability of the SUSY Auxiliary Field Problem, JHEP 04 (2015) 056 [arXiv:1502.04164] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  25. [25]
    M. Calkins, D.E.A. Gates, S.J. Gates and B. McPeak, Is it possible to embed a 4D, \( \mathcal{N} \) = 4 supersymmetric vector multiplet within a completely off-shell adinkra hologram?, JHEP 05 (2014) 057 [arXiv:1402.5765] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    C.F. Doran, M.G. Faux, S.J. Gates Jr., T. Hübsch, K.M. Iga and G.D. Landweber, On graph-theoretic identifications of Adinkras, supersymmetry representations and superfields, Int. J. Mod. Phys. A 22 (2007) 869 [math-ph/0512016] [INSPIRE].
  27. [27]
    C.F. Doran, M.G. Faux, S.J. Gates Jr., T. Hübsch, K.M. Iga and G.D. Landweber, Relating Doubly-Even Error-Correcting Codes, Graphs and Irreducible Representations of N-Extended Supersymmetry, arXiv:0806.0051 [INSPIRE].
  28. [28]
    C.F. Doran et al., Codes and Supersymmetry in One Dimension, Adv. Theor. Math. Phys. 15 (2011) 1909 [arXiv:1108.4124] [INSPIRE].CrossRefMATHMathSciNetGoogle Scholar
  29. [29]
    C.F. Doran et al., Topology Types of Adinkras and the Corresponding Representations of N-Extended Supersymmetry, arXiv:0806.0050 [INSPIRE].

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Center for String and Particle Theory-Dept. of PhysicsUniversity of MarylandCollege ParkU.S.A.
  2. 2.Department of PhysicsBrown UniversityProvidenceU.S.A.
  3. 3.Institute for Theoretical Physics and AstrophysicsMasaryk UniversityBrnoCzech Republic

Personalised recommendations