Skip to main content
SpringerLink
Log in

Superstring symmetries and space-time dimensionality

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

The value of the dimensionality \(\mathcal{D}\) of the physical space-time can be determined by the application of continuous and discrete symmetry principles to both the \(\mathcal{D}\)-dimensional effective action \(S_\mathcal{D}\) and the two-dimensional world-sheet action S 2 of the heterotic superstring theory. In particular, for a background Friedmann space-time generated by stringy matter with the equation of state \(p = - \rho /(\mathcal{D} - 1)\), we show here that the world sheet is only supersymmetric, and only invariant under the time-reversal operator T, if \(\mathcal{D} = 4\). This is the condition that \(S_\mathcal{D}\) is invariant under T, and also for the realization of the non-linear global supersymmetry due to Volkov and Akulov.

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. M.B. Green, J.H. Schwarz, E. Witten, Superstring Theory, Vols. 1,2 (Cambridge University Press, Cambridge, 1987).

  2. D.J. Gross, J.A. Harvey, E. Martinec, R. Rohm, Phys. Rev. Lett. 54, 502 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  3. D.J. Gross, J.A. Harvey, E. Martinec, R. Rohm, Nucl. Phys. B 256, 253 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  4. D.J. Gross, J.A. Harvey, E. Martinec, R. Rohm, Nucl. Phys. B 267, 75 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  5. P. Candelas, G.T. Horowitz, A. Strominger, E. Witten, Nucl. Phys. B 258, 46 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  6. B.R. Greene, K.H. Kirklin, P.J. Miron, G.G. Ross, Phys. Lett. B 180, 69 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  7. M.D. Pollock, Int. J. Mod. Phys. A 21, 373 (2006).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. M.D. Pollock, Int. J. Mod. Phys. A 28, 1392001(E) (2013).

    Article  ADS  MathSciNet  Google Scholar 

  9. M.D. Pollock, Int. J. Mod. Phys. A 24, 4373 (2009).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  10. D.V. Volkov, V.P. Akulov, Pis'ma Zh. Eksp. Teor. Fiz. 16, 621 (1972) (JETP Lett. 16.

    Google Scholar 

  11. D.V. Volkov, V.P. Akulov, Phys. Lett. B 46, 109 (1973).

    Article  ADS  Google Scholar 

  12. V.P. Akulov, D.V. Volkov, Teor. Mat. Fiz. 18, 39 (1974) (Theor. Math. Phys. 18.

    Article  MathSciNet  Google Scholar 

  13. M.D. Pollock, Int. J. Mod. Phys. A 7, 4149 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  14. M.D. Pollock, Int. J. Mod. Phys. A 27, 1292005(E) (2012).

    Article  ADS  MathSciNet  Google Scholar 

  15. M.D. Pollock, Int. J. Mod. Phys. A 16, 3217 (2001).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  16. M.D. Pollock, Int. J. Mod. Phys. A 27, 1292008(E) (2012).

    Article  ADS  MathSciNet  Google Scholar 

  17. M.D. Pollock, Int. J. Mod. Phys. D 11, 1409 (2002).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  18. M.D. Pollock, Int. J. Mod. Phys. D 17, 95 (2008).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  19. M.D. Pollock, Int. J. Mod. Phys. D 21, 1292001(E) (2012).

    Article  ADS  MathSciNet  Google Scholar 

  20. M.D. Pollock, Int. J. Mod. Phys. D 21, 1292004(E) (2012).

    Article  ADS  Google Scholar 

  21. K.M. Short, Class. Quantum Grav. 6, 1351 (1989).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  22. M.D. Pollock, Int. J. Mod. Phys. D 1, 407 (1992).

    Article  ADS  MATH  Google Scholar 

  23. M.D. Pollock, Int. J. Mod. Phys. D 5, 441(E) (1996).

    Article  ADS  MathSciNet  Google Scholar 

  24. M.D. Pollock, Int. J. Mod. Phys. D 4, 305 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  25. M.D. Pollock, Int. J. Mod. Phys. D 21, 1292002(E) (2012).

    Article  ADS  Google Scholar 

  26. J.A. Wheeler, in Battelle Rencontres, 1967 Lectures in Mathematics and Physics, edited by C.M. DeWitt, J.A. Wheeler (Benjamin, New York, 1968) p. 242.

  27. B.S. DeWitt, Phys. Rev. 160, 1113 (1967).

    Article  ADS  MATH  Google Scholar 

  28. C.L. Bennett et al., Astrophys. J. Suppl. Ser. 148, 1 (2003).

    Article  ADS  Google Scholar 

  29. E. Komatsu et al., Astrophys. J. Suppl. Ser. 180, 330 (2009).

    Article  ADS  Google Scholar 

  30. E. Witten, Phys. Lett. B 155, 151 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  31. G. Nordström, Proc. Kon. Ned. Akad. Wet. Amsterdam 20, 1076 (1918).

    ADS  Google Scholar 

  32. R.C. Tolman, Relativity, Thermodynamics and Cosmology (Clarendon Press, Oxford, 1934).

  33. E.A. Milne, Nature 130, 9 (1932) and Relativity Gravitation and World Structure.

    Article  ADS  Google Scholar 

  34. J.H. Schwarz, Phys. Rep. 89, 223 (1982).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  35. A. Dabholkar, G. Gibbons, J.A. Harvey, F. Ruiz Ruiz, Nucl. Phys. B 340, 33 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  36. M.D. Pollock, Mod. Phys. Lett. A 23, 797 (2008).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  37. G. Lüders, Ann. Phys. (New York) 2, 1 (1957).

    Article  ADS  MATH  Google Scholar 

  38. M.D. Pollock, Mod. Phys. Lett. A 23, 2665 (2008).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  39. A.M. Polyakov, Nucl. Phys. B 268, 406 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  40. H. Kleinert, Phys. Lett. B 174, 335 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  41. T.L. Curtright, P. van Nieuwenhuizen, Nucl. Phys. B 294, 125 (1987).

    Article  ADS  Google Scholar 

  42. W. Helfrich, Z. Naturforsch. 30c, 841 (1975).

    Google Scholar 

  43. L. Peliti, S. Leiblev, Phys. Rev. Lett. 54, 1690 (1985).

    Article  ADS  Google Scholar 

  44. D. Förster, Phys. Lett. A 114, 115 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  45. H. Kleinert, Phys. Lett. A 114, 263 (1986).

    Article  ADS  Google Scholar 

  46. M.D. Pollock, Int. J. Mod. Phys. D 6, 91 (1997).

    Article  ADS  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. V. A. Steklov Mathematical Institute, Russian Academy of Sciences, Ulitsa Gubkina 8, 119991, Moscow, Russia

    M. D. Pollock

Authors
  1. M. D. Pollock
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. D. Pollock.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pollock, M.D. Superstring symmetries and space-time dimensionality. Eur. Phys. J. Plus 129, 139 (2014). https://doi.org/10.1140/epjp/i2014-14139-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2014-14139-6

Keywords

Search

Navigation