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

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 
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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

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