Advertisement

Momentum space topology of fermion zero modes brane

  • G. E. Volovik
Gravity, Astrophysics

Abstract

We discuss fermion zero modes within the 3+1 brane, i.e., the domain wall between the two vacua in 4+1 spacetime. We do not assume relativistic invariance in 4+1 spacetime or any special form of the 4+1 action. The only input is that the fermions in bulk are fully gapped and are described by a nontrivial momentum-space topology. Then the 3+1 wall between such vacua contains chiral 3+1 fermions. The bosonic collective modes in the wall form the gauge and gravitational fields. In principle, this universality class of fermionic vacua can contain all the ingredients of the Standard Model and gravity.

PACS numbers

04.50.+h 11.25.Mj 11.27.+d 73.43.−f 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. A. Rubakov and M. E. Shaposhnikov, Phys. Lett. B 125, 136 (1983); K. Akama, in Lecture Notes in Physics, Vol. 176: Gauge Theory and Gravitation, Ed. by K. Kikkawa, N. Nakanishi, and H. Nariai (Springer-Verlag, Berlin, 1983), pp. 267–271; K. Akama, hep-th/0001113.ADSGoogle Scholar
  2. 2.
    T. Kaluza, Sitzungsber. K. Preuss. Akad. Wiss. K1, 966 (1921).Google Scholar
  3. 3.
    O. Klein, Z. Phys. 37, 895 (1926).zbMATHGoogle Scholar
  4. 4.
    L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999).ADSMathSciNetGoogle Scholar
  5. 5.
    C. D. Hoyle, U. Schmidt, B. R. Heckel, et al., Phys. Rev. Lett. 86, 1418 (2001).CrossRefADSGoogle Scholar
  6. 6.
    S. C. Zhang and J. Hu, Science 294, 823 (2001).CrossRefADSGoogle Scholar
  7. 7.
    B. I. Halperin, Phys. Rev. B 25, 2185 (1982); X. G. Wen, Phys. Rev. Lett. 64, 2206 (1990); M. Stone, Phys. Rev. B 42, 8399 (1990).CrossRefADSMathSciNetGoogle Scholar
  8. 8.
    G. E. Volovik, Phys. Rep. 351, 195 (2001).CrossRefADSzbMATHMathSciNetGoogle Scholar
  9. 9.
    G. E. Volovik, in Proceedings of the XVIII CFIF Autumn School “Topology of Strongly Correlated Systems”, Lisbon, 2000 (World Scientific, Singapore, 2001), p. 30; cond-mat/0012195.Google Scholar
  10. 10.
    G. E. Volovik and V. M. Yakovenko, J. Phys.: Condens. Matter 1, 5263 (1989).CrossRefADSGoogle Scholar
  11. 11.
    M. Kohmoto, Ann. Phys. 160, 343 (1985).MathSciNetGoogle Scholar
  12. 12.
    K. Ishikawa and T. Matsuyama, Z. Phys. C 33, 41 (1986); Nucl. Phys. B 280, 523 (1987); T. Matsuyama, Prog. Theor. Phys. 77, 711 (1987).CrossRefGoogle Scholar
  13. 13.
    M. F. Atiyah and I. M. Singer, Ann. Math. 87, 484 (1968); 93, 119 (1971).MathSciNetGoogle Scholar
  14. 14.
    G. E. Volovik, Pis’ma Zh. Éksp. Teor. Fiz. 66, 492 (1997) [JETP Lett. 66, 522 (1997)].Google Scholar
  15. 15.
    R. Laughlin and D. Pines, Proc. Natl. Acad. Sci. USA 97, 28 (2000).ADSMathSciNetGoogle Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2002

Authors and Affiliations

  • G. E. Volovik
    • 1
    • 2
  1. 1.Low Temperature LaboratoryHelsinki University of TechnologyFinland
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

Personalised recommendations