Advertisement

Think different: applying the old macintosh mantra to the computability of the SUSY auxiliary field problem

  • Mathew Calkins
  • D. E. A. Gates
  • S. James GatesJr.
  • William M. Golding
Open Access
Regular Article - Theoretical Physics

Abstract

Starting with valise supermultiplets obtained from 0-branes plus field redefinitions, valise adinkra networks, and the “Garden Algebra,” we discuss an architecture for algorithms that (starting from on-shell theories and, through a well-defined computation procedure), search for off-shell completions. We show in one dimension how to directly attack the notorious “off-shell auxiliary field” problem of supersymmetry with algorithms in the adinkra network-world formulation.

Keywords

Space-Time Symmetries Gauge Symmetry Global Symmetries 

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]
    W. Siegel and M. Roček, On off-shell supermultiplets, Phys. Lett. B 105 (1981) 275 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    S.J. Gates Jr. and S. Vashakidze, On D = 10, N = 1 Supersymmetry, Superspace Geometry and Superstring Effects, Nucl. Phys. B 291 (1987) 172 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    E. Bergshoeff, M. Rakowski and E. Sezgin, Higher derivative super Yang-Mills theories, Phys. Lett. B 185 (1987) 371 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    K. Peeters, P. Vanhove and A. Westerberg, Supersymmetric R 4 actions and quantum corrections to superspace torsion constraints, hep-th/0010182 [INSPIRE].
  5. [5]
    M. Cederwall, B.E.W. Nilsson and D. Tsimpis, The Structure of maximally supersymmetric Yang-Mills theory: Constraining higher order corrections, JHEP 06 (2001) 034 [hep-th/0102009] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    S.F. Kerstan, Supersymmetric Born-Infeld from the D9-brane, Class. Quant. Grav. 19 (2002) 4525 [hep-th/0204225] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    N. Berkovits and V. Pershin, Supersymmetric Born-Infeld from the pure spinor formalism of the open superstring, JHEP 01 (2003) 023 [hep-th/0205154] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    S.J. Gates and L. Rana, A Theory of spinning particles for large-N extended supersymmetry, Phys. Lett. B 352 (1995) 50 [hep-th/9504025] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    S.J. Gates Jr. and L. Rana, A Theory of spinning particles for large-N extended supersymmetry. 2., Phys. Lett. B 369 (1996) 262 [hep-th/9510151] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    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
  11. [11]
    C.F. Doran et al., On graph-theoretic identifications of Adinkras, supersymmetry representations and superfields, Int. J. Mod. Phys. A 22 (2007) 869 [math-ph/0512016] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    C.F. Doran et al., Relating Doubly-Even Error-Correcting Codes, Graphs and Irreducible Representations of N-Extended Supersymmetry, arXiv:0806.0051 [INSPIRE].
  13. [13]
    C.F. Doran et al., Codes and Supersymmetry in One Dimension, Adv. Theor. Math. Phys. 15 (2011) 1909 [arXiv:1108.4124] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    C.F. Doran et al., Topology Types of Adinkras and the Corresponding Representations of N-Extended Supersymmetry, arXiv:0806.0050 [INSPIRE].
  15. [15]
    Y. Zhang, Adinkras for Mathematicians, Trans. Am. Math. Soc. 366 (2014) 3325.MathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    S.J. Gates Jr., The Search for Elementarity Among Off-Shell SUSY Representations, The Korean Institute for Advanced Studies (KIAS) Newsletter 5 (2012) 19.Google Scholar
  17. [17]
    I. Chappell, Isaac, S.J. Gates and T. Hübsch, Adinkra (in)equivalence from Coxeter group representations: A case study, Int. J. Mod. Phys. A 29 (2014) 1450029 [arXiv:1210.0478] [INSPIRE].
  18. [18]
    C. Doran, K. Iga, G. Landweber and S. Mendez-Diez, Geometrization of N-Extended 1-Dimensional Supersymmetry Algebras, arXiv:1311.3736 [INSPIRE].
  19. [19]
    S.J. Gates Jr. and L. Rana, On Extended Supersymmetric Quantum Mechanics, UMDEPP 93-194 (1994), unpublished.Google Scholar
  20. [20]
    S.J. Gates Jr. and L. Rana, Ultramultiplets: A New representation of rigid 2-d, N = 8 supersymmetry, Phys. Lett. B 342 (1995) 132 [hep-th/9410150] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    S.J. Gates Jr. and L. Rana, Tuning the RADIO to the off-shell 2-D Fayet hypermultiplet problem, hep-th/9602072.
  22. [22]
    S.J. Gates Jr., S. Randall and K. Stiffler, Reduction Redux of Adinkras, Int. J. Mod. Phys. A 29 (2014) 1450070 [arXiv:1312.2000] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  23. [23]
    J. Gates et al., 4D, N = 1 Supersymmetry Genomics (I), JHEP 12 (2009) 008 [arXiv:0902.3830] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    S.J. Gates, T. Hubsch and K. Stiffler, On Clifford-AlgebraicHoloraumy, Dimensional Extension and SUSY Holography, arXiv:1409.4445 [INSPIRE].
  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]
    S.J. Gates Jr., J. Parker, V.G.J. Rodgers, L. Rodriguez and K. Stiffler, A Detailed Investigation of First and Second Order Supersymmetries for Off-Shell N = 2 and N = 4 Supermultiplets, arXiv:1106.5475 [INSPIRE].
  27. [27]
    S.J. Gates and L. Rana, A Theory of spinning particles for large-N extended supersymmetry, Phys. Lett. B 352 (1995) 50 [hep-th/9504025] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    S.J. Gates Jr. and L. Rana, A Theory of spinning particles for large-N extended supersymmetry. 2., Phys. Lett. B 369 (1996) 262 [hep-th/9510151] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
  30. [30]
    M. Calkins, D.E.A. Gates, S.J. Gates and K. Stiffler, Adinkras, 0-branes, Holoraumy and the SUSY QFT/QM Correspondence, arXiv:1501.00101 [INSPIRE].

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Mathew Calkins
    • 1
  • D. E. A. Gates
    • 1
  • S. James GatesJr.
    • 1
  • William M. Golding
    • 2
  1. 1.Center for String and Particle Theory, Department of PhysicsUniversity of MarylandCollege ParkUnited States
  2. 2.Sensors and Electron Devices DirectorateUS Army Research LaboratoryAdelphiUnited States

Personalised recommendations