Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 4 (2008), 025, 14 pages      arXiv:0802.3445      https://doi.org/10.3842/SIGMA.2008.025
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Free Field Construction of D-Branes in Rational Models of CFT and Gepner Models

Sergei E. Parkhomenko
Landau Institute for Theoretical Physics Chernogolovka, Russia

Received October 30, 2007, in final form February 14, 2008; Published online February 23, 2008

Abstract
This is a review article of my recent papers on free field construction of D-branes in N = 2 superconformal minimal models and Gepner models.

Key words: strings; D-branes; conformal field theory; free field construction; minimal models; Gepner models.

pdf (268 kb)   ps (182 kb)   tex (18 kb)

References

  1. Polchinski J., Dirichlet branes and Ramond-Ramond charges, Phys. Rev. Lett. 75 (1995), 4724-4727, hep-th/9510017.
    Polchinski J., TASI lectures on D-branes, hep-th/9611050.
  2. Gepner D., Space-time supersymmetry in compactified string theory and superconformal models, Nuclear Phys. B 296 (1988), 757-778.
  3. Feigin B.L., Fuchs D.B., Invariant skew-symmetric differential operators on line and Verma modules over the Virasoro algebra, Funct. Anal. Appl. 16 (1982), 114-126.
    Feigin B.L., Fuchs D.B., Representations of Virasoro algebra, in Seminar on Supermanifolds 5, Editors D. Leites, Reports of Dept. Math. Stockholm Univ., 1986.
  4. Malikov F.G., Feigin B.L., Fuchs D.B., Singular vectors in Verma modules over Kac-Moody algebras, Funktsional. Anal. i Prilozhen. 20 (1986), no. 2, 25-37, 96 (in Russian).
  5. Feigin B.L., Frenkel E., Representations of affine Kac-Moody algebras and bosonization, Physics and Mathematics of Strings, Vol. 271, World Sci. Publishing, Teaneck, 1990.
    Feigin B.L., Frenkel E., Affine Kac-Moody algebras and semi-infinite flag manifolds, Comm. Math. Phys. 128 (1990), 161-189.
  6. Felder G., BRS Approach to minimal models, Nuclear Phys. B 317 (1989), 215-236.
    Bernard D., Felder G., Fock representations and BRSt cohomology in SL(2) current algebra, Comm. Math. Phys. 127 (1990), 145-168.
  7. Dotsenko V.S., Fateev V.A., Conformal algebra and multipoint correlation functions in 2D statistical models, Nuclear Phys. B 240 (1984). 312-348.
    Dotsenko V.S., Fateev V.A., Four point correlation functions and operator algebra in 2D conformal invariant field theory with central charge c < 1, Nuclear Phys. B 251 (1985), 691-734.
  8. Dotsenko V.S., Solving the SU(2) conformal field theory using the Wakimoto free field representation, Nuclear Phys. B 358 (1991), 547-570.
  9. Parkhomenko S.E., BRST construction of D-branes in SU(2) WZW model, Nuclear Phys. B 617 (2001), 198-214, hep-th/0103142.
  10. Parkhomenko S.E., Free field construction of D-branes in N = 2 minimal models, Nuclear Phys. B 671 (2003), 325-342, hep-th/0301070.
  11. Parkhomenko S.E., Free field approach to D-branes in Gepner models, Nuclear Phys. B 731 (2005), 360-388, hep-th/0412296.
  12. Parkhomenko S.E., Free field representation of permutation D-branes in Gepner models, J. Exp. Theor. Phys. 102 (2006), 902-919, hep-th/0512322.
  13. Ishikawa H., Watamura S., Free field realization of D-brane in group manifold, J. High Energy Phys. 2000 (2000), no. 8, 044, 23 pages, hep-th/0007141.
  14. Feigin B.L., Semikhatov A.M., Sirota V.A., Tipunin I.Yu., Resolutions and characters of irredicible representations of the N = 2 superconformal algebra, Nuclear Phys. B 536 (1998), 617-656, hep-th/9805179.
  15. Schwimmer A., Seiberg N., Comments on the N = 2,3,4 superconformal algebras in two dimensions, Phys. Lett. B 184 (1987), 191-196.
  16. Feigin B.L., Semikhatov A.M., Free field resolutions of the unitary N = 2 super-Virasoro representations, hep-th/9810059.
  17. Cardy J.L., Boundary conditions, fusion rules and the Verlinde formula, Nuclear Phys. B 324 (1989), 581-596.
  18. Sen A., Tachyon condensation on the brane antibrane system, J. High Energy Phys. 1998 (1998), no. 8, 012, 6 pages, hep-th/9805170.
  19. Gelfand S., Manin Yu., Methods of homological algebra, Springer-Verlag, Berlin, 1996.
  20. Okuda T., Takayanagi T., Ghost D-branes, J. High Energy Phys. 2006 (2006), no. 3, 062, 39 pages, hep-th/0601024.
  21. Recknagel A., Schomerus V., D-branes in Gepner models, Nuclear Phys. B 531 (1998), 185-225, hep-th/9712186.
  22. Eguchi T., Ooguri H., Taormina A., Yang S.-K., Superconformal algebras and string compactification on manifolds with SU(n) holonomy, Nuclear Phys. B 315 (1989) 193-221.
  23. Fuchs J., Schweigert C., Walcher J., Projections in string theory and boundary states for Gepner models, Nuclear Phys. B 588 (2000), 110-148, hep-th/0003298.
  24. Recknagel A., Permutation branes, J. High Energy Phys. 2003 (2003), no. 4, 041, 27 pages, hep-th/0208119.
  25. Malikov F., Schechtman V., Vaintrob A., Chiral de Rham complex, Comm. Math. Phys. 204 (1999), 439-473, math.AG/9803041.
  26. Frenkel E., Schestney M., Chiral de Rham complex on orbifolds, math.AG/0307181.
  27. Diaconescu D., Gomis J., Fractional branes and boundary states in orbifold theories, J. High Energy Phys. 2000 (2000), no. 10, 001, 48 pages, hep-th/9906242.

Previous article   Next article   Contents of Volume 4 (2008)