Skip to main content
SpringerLink
Log in

World crystal: extending to four dimensional

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

Dislocation condensation in (2+1)-dimensional World crystal can lead to an emerging linearized gravitation. In this note, we extend the (2+1)D world crystal model to 4-dimensional. By defining the density tensors of defect surfaces in 4-dimensional crystals, we establish the defect field theory of 4D crystal. We present that the proliferation of dislocation surfaces in the 4D world crystal also results in the emergence of linearized gravitation.

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. Schwarz J.H., Seiberg N.: Rev. Mod. Phys. 71, 112 (1999)

    Article  Google Scholar 

  2. Banks, T.: arXiv:hep-th/0306074

  3. Schellekens A.N.: Rep. Prog. Phys. 71, 072201 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  4. Zhang, S.C.: arXiv:hep-th/0204061

  5. Jacobson T.: Phys. Rev. Lett. 75, 1260 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Volovik G.E.: The Universe in a Helium Droplet. Oxford University Press, Oxford (2003)

    MATH  Google Scholar 

  7. Wu S.F., Wang B., Yang G.H., Zhang P.M.: Class. Quant. Gravit. 25, 235018 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  8. Parikh, M., Sarkar, S.: arXiv:0903.1176 (2009)

  9. Padmanabhan, T.: arXiv:0903.1254 (2009)

  10. Cai R.G., Cao L.M.: Nucl. Phys. B 785, 135 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Eling C., Guedens R., Jacobson T.: Phys. Rev. Lett. 96, 121301 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  12. Chapline, G., Hohlfeld, E., Laughlin, R.B., Santiago, D.I.: arXiv:gr-qc/0012094.

  13. Volovik G.E.: Phys. Rep. 351, 195 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Volovik, G.E.: arXiv:gr-qc/0304061

  15. Gu, Z.C., Wen, X.G.: arXiv:gr-qc/0606100

  16. ’t Hooft G.: Int. J. Mod. Phys. A 24, 3243 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Padmanabhan T., Paranjape A.: Phys. Rev. D75, 064004 (2007)

    MathSciNet  ADS  Google Scholar 

  18. Wu S.F., Wang B., Ge X.H., Yang G.H.: Phys. Rev. D81, 044010 (2010)

    ADS  Google Scholar 

  19. Kleinert H.: Gauge Fields in Condensed Matter, vols I and II. World Scientific, Singapore (1989)

    Google Scholar 

  20. Kleinert H.: Ann. Phys. 44, 117 (1987)

    Article  Google Scholar 

  21. Kleinert H., Zaanen J.: Phys. Lett. A 324, 361 (2004)

    Article  ADS  MATH  Google Scholar 

  22. Zaanen J., Nussinov Z., Mukhin S.I.: Ann. Phys. (NY) 310, 181 (2204)

    Article  Google Scholar 

  23. Cvektovic V., Zaanen J.: Phys. Rev. Lett. 97, 045701 (2006)

    Article  ADS  Google Scholar 

  24. Cvektovic V., Nussinov Z., Mukhin S., Zaanen J.: EPL 81, 27001 (2008)

    Article  ADS  Google Scholar 

  25. Cvektovic V., Nussinov Z., Zaanen J.: Phil. Mag. 86, 2995 (2006)

    Article  ADS  Google Scholar 

  26. Nielsen H., Olesen P.: Nucl. Phys. B 61, 45 (1973)

    Article  ADS  Google Scholar 

  27. Beekman A.J., Sadri D., Zaanen J.: New J. Phys. 13, 033004 (2011)

    Article  ADS  Google Scholar 

  28. Kleinert H.: Multivalued Fields in Condensed Matter, Electromagnism, and Gravitation. World Scientific, Singapore (2008)

    Google Scholar 

  29. Jiang Y., Duan Y.S.: J. Math. Phys. 41, 2616 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Yi Zhu & Ying Jiang

  2. Key Lab for Astrophysics, Shanghai, 200234, People’s Republic of China

    Ying Jiang

Authors
  1. Yi Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ying Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ying Jiang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhu, Y., Jiang, Y. World crystal: extending to four dimensional. Gen Relativ Gravit 43, 2935–2941 (2011). https://doi.org/10.1007/s10714-011-1215-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10714-011-1215-5

Keywords

Search

Navigation