Advertisement

Theoretical and Mathematical Physics

, Volume 139, Issue 3, pp 834–845 | Cite as

The Poisson–Lie T-Duality and Zero Modes

  • C. Klimčík
  • S. E. Parkhomenko
Article

Abstract

We consider the Lu–Weinstein–Soibelman Drinfeld double D and a pair of σ-models associated with it. We show that the Poisson–Lie T-duality relating them can be extended to include string configurations with a nonunit non-Abelian momentum. The dual string configuration (living on the maximal compact subgroup of D) then develops a nontrivial monodromy taking values in the Weyl alcove. We also give the duality-invariant action of this dynamical system and describe the analogous phenomenon for the dressing cosets.

strings σ-model T-duality 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    C. Klimčík and P. Ševera, Phys. Lett. B, 383, 281 (1996).Google Scholar
  2. 2.
    C. Klimčík and P. Ševera, Phys. Lett. B, 351, 455 (1995); C. Klimčík, Nucl. Phys. B (Proc. Suppl.), 46, 116 (1996); P. Ševera, “Minimálne plochy a dualita,” Diploma thesis, Praha University, Prague (1995).Google Scholar
  3. 3.
    J.-H. Lu and A. Weinstein, J. Differential Geom., 31, 510 (1990); Ya. S. Soibelman, Leningrad Math. J., 2, 161 (1990).Google Scholar
  4. 4.
    K. Kikkawa and M. Yamasaki, Phys. Lett. B, 149, 357 (1984); N. Sakai and I. Senda, Prog. Theoret. Phys., 75, 692 (1986).Google Scholar
  5. 5.
    C. Klimčík and S. Parkhomenko, Phys. Lett. B, 463, 195 (1999).Google Scholar
  6. 6.
    C. Klimčík and P. Ševera, Phys. Lett. B, 372, 65 (1996).Google Scholar
  7. 7.
    K. Sfetsos, Nucl. Phys. B, 517, 549 (1988).Google Scholar
  8. 8.
    M. Blau and G. Thompson, “Lectures on 2d gauge theories: Topological aspects and path integral techniques,” in: Proc. 1993 Trieste Summer School on High Energy Physics and Cosmology (E. Gava et al., eds.), World Scientific, Singapore (1994), p. 175; hep-th/9310144 (1993).Google Scholar
  9. 9.
    F. Falceto and K. Gawedzki, J. Geom. Phys., 11, 251 (1993).Google Scholar
  10. 10.
    A. Polyakov and P. B. Wiegmann, Phys. Lett. B, 311, 549 (1983).Google Scholar
  11. 11.
    H. Flaschka and T. Ratiu, Ann. Sci. École Norm. Sup. (4), 29, 787 (1996).Google Scholar
  12. 12.
    C. Klimčík and P. Ševera, Phys. Lett. B, 381, 56 (1996).Google Scholar
  13. 13.
    X. de la Ossa and F. Quevedo, Nucl. Phys. B, 403, 377 (1993); B. E. Fridling and A. Jevicki, Phys. Lett. B, 134, 70 (1984); E. S. Fradkin and A. A. Tseytlin, Ann. Phys., 162, 31 (1985).Google Scholar
  14. 14.
    K. Sfetsos, Nucl. Phys. B (Proc. Suppl.), 56, 302 (1997); Phys. Rev. D, 57, 3585 (1998); M. A. Lledo and V. S. Varadarajan, Lett. Math. Phys., 45, 247 (1998); S. Parkhomenko, Nucl. Phys. B, 510, 623 (1998); A. Stern, Phys. Lett. B, 450, 141 (1999); Nucl. Phys. B, 557, 459 (1999); M. A. Jafarizadeh and A. Rezaei-Aghdam, Phys. Lett. B, 45, 477 (1999); E. J. Beggs and S. Majid, “Poisson–Lie T-duality for quasitriangular Lie bialgebras,” math.QA/9906040 (1999); O. Alvarez, Nucl. Phys. B, 584, 659, 682 (2000); F. Assaoui, N. Benhamou, and T. Lhallabi, “Poisson–Lie T-duality in supersymmetric WZNW model,” hep-th/0009024 (2000).Google Scholar
  15. 15.
    A. Alekseev, C. Klimčík, and A. Tseytlin, Nucl. Phys. B, 458, 430 (1996); E. Tyurin and R. von Unge, Phys. Lett. B, 382, 233 (1996); P. Ševera, JHEP, 0205, 049 (2002); hep-th/9803201 (1998); K. Sfetsos, Phys. Lett. B, 432, 365 (1998); L. K. Balazs, J. Balog, P. Forgacs, N. Mohammedi, L. Palla, and J. Schnittger, Nucl. Phys. B, 535, 461 (1998); S. Parkhomenko, JETP, 89, 5 (1999).Google Scholar

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • C. Klimčík
    • 1
  • S. E. Parkhomenko
    • 1
    • 2
  1. 1.Institute de Mathématiques de LuminyMarseilleFrance
  2. 2.Landau Institute for Theoretical PhysicsChernogolovka, Moscow OblastRussia

Personalised recommendations