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The geometrical properties and physical meaning of some particular Riemannian superspaces

  • Physics of Elementary Particles and Atomic Nuclei. Theory
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Abstract

The geometrical meaning of a particularly simple metric in the superspace is elucidated, and their possible connection with mechanisms of topological origin in high energy physics, i.e., the localization of the fields in a particular sector of supermanifold, is analyzed and discussed. The description and the analysis of some interesting aspects of the simplest Riemannian superspaces are presented from the point of view of possible vacuum solutions.

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References

  1. V. P. Akulov, V. A. Soroka, and D. V. Volkov, Pis’ma Zh. Eksp. Teor. Fiz. 22, 396 (1975) [JETP Lett. 22, 187 (1975)]; Theor. Math. Phys. 31, 12 (1977); B. Zumino, Preprint No. TH2120 (CERN, 1975); J. Wess and B. Zumino, Phys. Lett. B 66, 61 (1977).

    Google Scholar 

  2. R. Arnowitt, P. Nath, and B. Zumino, Nucl. Phys. B 56,81 (1975).

    MathSciNet  Google Scholar 

  3. V. Ogievetsky and E. Sokatchev, Phys. Lett. B 79, 222(1978).

    Article  ADS  Google Scholar 

  4. W. Siegel and S. J. Gates, Jr., Nucl. Phys. B 147, 77(1978).

    Article  ADS  Google Scholar 

  5. I. L. Buchbinder and S. M. Kuzenko, Ideas and Methods of Supersymmetry and Supergravity (IOP Publ., Philadelphia, 1995); B. de Witt, Supermanifolds (Cambridge Univ. Press, Cambridge, 1984).

    MATH  Google Scholar 

  6. S. B. Giddings and A. Maharana, Phys. Rev. D: Part. Fields 73, 126003 (2006); K. Koyama, Gen. Rel. Grav. 40, 421 (2008).

    Google Scholar 

  7. T. Curtright et al., JHEP 0704.020 (2007).

  8. S. Bellucci et al., Phys. Rev. D: Part. Fields 66, 086001 (2002).

    Google Scholar 

  9. A. I. Pashnev and D. V. Volkov, Teor. Mat. Fiz. 44(3), 321 (1980).

    MathSciNet  Google Scholar 

  10. D. J. Cirilo-Lombardo, Part. Nucl. Lett. 4(3), 239 (2007); Foundations of Phys. 37 (6), (2007).

    Article  MathSciNet  Google Scholar 

  11. D. J. Cirilo-Lombardo, Rom. J. Phys. 50, 875 (2005); Part. Nucl. Lett. 3, 416 (2006); Hadronic J. 29, 355 (2006).

    MathSciNet  Google Scholar 

  12. V. P. Akulov and D. V. Volkov, Theor. Math. Phys. 41,939 (1979).

    Article  MathSciNet  Google Scholar 

  13. V. P. Akulov and D. V. Volkov, Theor. Math. Phys. 42, 10(1980).

    Article  MathSciNet  Google Scholar 

  14. B. Bajc and G. Gabadadze, Phys. Lett. B 474, 282 (2000).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. O. Bertolami et al., Intern. J. Mod. Phys. A 6, 4149 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  16. D. J. Cirilo-Lombardo, (in preparation).

  17. D. Alfaro, S. Fubini, and G. Furlan, Nuovo Cim. A 34, 569 (1976).

    Article  ADS  Google Scholar 

  18. R. Arnowitt and P. Nath, Phys. Rev. D: Part. Fields 15, 1033 (1977).

    ADS  MathSciNet  Google Scholar 

  19. J. R. Klauder and B. S. Skagerstam, Coherent States (World Sci., Singapore, 1985).

    MATH  Google Scholar 

  20. N. Arkani-Hamed et al., Phys. Lett. B 429, 263 (1998); Phys. Rev. D 59, 0860 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  21. V. A. Rubakov and M. E. Shaposhnikov, Phys. Lett. B 125, 136 (1983).

    Article  ADS  Google Scholar 

  22. G. Dvali and M. Shifman, Phys. Lett. B 396, 64 (1997); Nucl. Phys. B 504, 127 (1996).

    Article  ADS  Google Scholar 

  23. J. Polchinski, Phys. Rev. Lett. 75, 4724 (1995).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  24. M. Gogberashvili, Int. J. Mod. Phys. D 11, 1635 (2002); Europhys. Lett. 49, 396 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  25. L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370, 4690 (1999).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  26. M. Gabella et al., Phys. Rev. D: Part. Fields 76, 055001 (2007).

    Google Scholar 

  27. F. Constantinescu, J. Phys. A: Math. Gen. 38, 1385(2005).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  28. S. S. Sannikov, “Non-Compact Symmetry Group of a Quantum Oscillator,” Zh. Eksp. Teor. Fiz. 49, 1913 (1965) [Sov. Phys. JETP 22, 1306 (1965)].

    MathSciNet  Google Scholar 

  29. T. Goldman et al., Phys. Lett. B 171, 217 (1986); M. M. Nieto, private commun.

    Article  ADS  Google Scholar 

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Correspondence to D. J. Cirilo-Lombardo.

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Cirilo-Lombardo, D.J. The geometrical properties and physical meaning of some particular Riemannian superspaces. Phys. Part. Nuclei Lett. 5, 494–500 (2008). https://doi.org/10.1134/S1547477108060022

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  • DOI: https://doi.org/10.1134/S1547477108060022

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