Skip to main content
SpringerLink
Log in

4D, \( \mathcal{N} \) = 1 supersymmetry genomics (II)

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We continue the development of a theory of off-shell supersymmetric representations analogous to that of compact Lie algebras such as SU(3). For off-shell 4D, \( \mathcal{N} \) = 1 systems, quark-like representations have been identified [1] in terms of cis-Adinkras and trans-Adinkras and it has been conjectured that arbitrary representations are composites of n c -cis and n t -trans representations. Analyzing the real scalar and complex linear super-field multiplets, these “chemical enantiomer” numbers are found to be n c  = n t  = 1 and n c  = 1, n t  = 2, respectively.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S.J. Gates Jr. et al., 4D, N = 1 Supersymmetry Genomics (I), JHEP 12 (2009) 008 [arXiv:0902.3830] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. M.B. Green, J.H. Schwarz and E. Witten, Superstring Theory. Vol. 2, Cambridge University Press, Cambridge U.K. (1987).

  3. J. Polchinski, String Theory. Vol. II: Superstring Theory and Beyond, Cambridge University Press, Cambridge U.K. (1998).

  4. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1133] [hep-th/9711200] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  5. O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. W. Siegel and M. Roček, On off-shell supermultiplets, Phys. Lett. B 105 (1981) 275 [INSPIRE].

    Article  ADS  Google Scholar 

  7. S.J. Gates Jr. et al., A detailed Investigation of First and Second Order Supersymmetries for Off-Shell N = 2 and N = 4 Supermultiplets, arXiv:1106.5475 [INSPIRE].

  8. 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].

    Article  MathSciNet  ADS  Google Scholar 

  9. E. Bergshoeff, M. de Roo and B. de Wit, Extended conformal supergravity, Nucl. Phys. B 182 (1981) 173 [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  11. Y.X. Zhang, Adinkras for mathematicians, arXiv:1111.6055 [INSPIRE].

  12. M. Faux, K. Iga and G. Landweber, Dimensional enhancement via supersymmetry, Adv. Math. Phys. 2011 (2011) 259089 [arXiv:0907.3605] [INSPIRE].

    MathSciNet  Google Scholar 

  13. M.G. Faux and G.D. Landweber, Spin holography via dimensional enhancement, Phys. Lett. B 681 (2009) 161 [arXiv:0907.4543] [INSPIRE].

    Article  ADS  Google Scholar 

  14. C. Doran et al., Adinkras and the Dynamics of Superspace Prepotentials, hep-th/0605269 [INSPIRE].

  15. C. Doran et al., Relating Doubly-Even Error-Correcting Codes, Graphs and Irreducible Representations of N-Extended Supersymmetry, arXiv:0806.0051 [INSPIRE].

  16. S.J. Gates Jr. and T. Hubsch, On Dimensional Extension of Supersymmetry: From Worldlines to Worldsheets, arXiv:1104.0722 [INSPIRE].

  17. H. Georgi, Lie Algebras in Particle Physics, second edition, Perseus Books, New York U.S.A. (1999).

  18. J.R. Silvester, Determinants of Block Matrices, Math. Gaz. 84 (2000) 460.

    Article  Google Scholar 

  19. D.Z. Freedman, Gauge Theories of Antisymmetric Tensor Fields, Caltech. preprint calt-68-624 (1977), unpublished.

Download references

Author information

Authors and Affiliations

  1. Center for String and Particle Theory, Department of Physics, University of Maryland, College Park, MD, 20742-4111, U.S.A

    S. James Gates Jr, James Parker & Kory Stiffler

  2. Department of Mathematics, Williams College, Williamstown, MA, 01267, U.S.A

    Jared Hallett

  3. Department of Physics and Astronomy, University of Iowa, Iowa City, IA, 52242, U.S.A

    Vincent G. J. Rodgers

Authors
  1. S. James Gates Jr
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jared Hallett
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. James Parker
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vincent G. J. Rodgers
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kory Stiffler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kory Stiffler.

Additional information

ArXiv ePrint: 1112.2147

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gates, S.J., Hallett, J., Parker, J. et al. 4D, \( \mathcal{N} \) = 1 supersymmetry genomics (II). J. High Energ. Phys. 2012, 71 (2012). https://doi.org/10.1007/JHEP06(2012)071

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2012)071

Keywords

Search

Navigation