The D-Brane Charges of C3/\(\mathbb{Z}_{2}\)

  • Elaine Beltaos
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 111)


The charges of WZW D-branes form a finite abelian group called the charge group. One approach to finding these groups is to use the conformal field theory description of D-branes, i.e. the charge equation. Using this approach, we work out the charge groups for the non-simply connected group \(C_{3}/\mathbb{Z}_{2}\), which requires knowing the NIM-rep of the underlying conformal field theory.


Conformal Field Theory Charge Group Fundamental Weight Charge Equation Fusion Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The author wishes to thank the organizers of the workshop for their kind hospitality and stimulating work environment during the workshop.


  1. 1.
    Alekseev, A., Schomerus, V.: RR charges of D2-branes in the WZW model (2000). arXiv:hep-th/0007096Google Scholar
  2. 2.
    Beltaos, E.: Fixed point factorization. In: Proceedings IX International Workshop on Lie Theory and its Applications to Physics, Springer Proceedings in Mathematics and Statistics, vol. 36, pp. 511–519. Springer, Tokyo/Heidelberg (2013)Google Scholar
  3. 3.
    Bouwknegt, P., Dawson, P., Ridout, D.: D-branes on group manifolds and fusion rings. J. High Energy Phys. 12, 065 (2002)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Braun, V., Sch\(\ddot{\text{a}}\) fer-Nameki, S.: Supersymmetric WZW models and twisted K-theory of SO(3). Adv. Theor. Math. Phys. 12, 217 (2008)Google Scholar
  5. 5.
    Fredenhagen, S.: D-brane charges on SO(3). J. High Energy Phys. 11, 082 (2004)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Fredenhagen, S., Schomerus, V.: Branes on group manifolds, gluon condensates, and twisted K-theory. J. High Energy Phys. 0104, 007 (2001)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Fuchs, J.: Simple WZW currents. Commun. Math. Phys. 136, 345 (1991)CrossRefMATHGoogle Scholar
  8. 8.
    Gaberdiel, M.R., Gannon, T.: Boundary states for WZW models. Nucl. Phys. B639, 471 (2002)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Gaberdiel, M.R., Gannon, T.: D-brane charges on non-simply connected groups. J. High Energy Phys. 04 030 (2004)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Gaberdiel, M.R., Gannon, T.: Twisted brane charges for non-simply connected groups. J. High Energy Phys. 035, 1 (2007)MathSciNetGoogle Scholar
  11. 11.
    Gannon, T.: Modular data: the algebraic combinatorics of rational conformal field theory. J. Alg. Combin. 22, 211 (2005)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Kac, V.G., Peterson, D.: Infinite-dimensional Lie algebras, theta functions and modular forms. Adv. Math. 53, 125 (1984)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Minasian, R., Moore, G.W.: K-theory and Ramond–Ramond charge. J. High Energy Phys. 11, 002 (1997)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Moore, G.W.: K-theory from a physical perspective (2003). arXiv:hep-th/0304018Google Scholar
  15. 15.
    Polchinski, J.: Tasi lectures on D-branes (1997). arXiv:hep-th/9611050v2Google Scholar
  16. 16.
    Witten, E.: D-branes and K-theory. J. High Energy Phys. 12, 019 (1998)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Grant MacEwan UniversityEdmontonCanada

Personalised recommendations