Presentations of Wess-Zumino-Witten fusion rings

Reviews in Mathematical Physics

Volumn 18, Issue 2, 2006, Pages 201-232

  Bouwknegt, Peter ^a   Ridout, David ^b,c  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b UNIVERSITY OF ADELAIDE   (Australia)

^c LA TROBE UNIVERSITY   (Australia)

Author keywords

Character; Conformal field theory; D brane; Fusion ring; Jacobi Trudy

Indexed keywords

EID: 33646471955     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X06002620     Document Type: Article

References (33)

1. E. Verlinde, Fusion rules and modular transformations in 2D conformal field theory, Nucl. Phys. B 300 (1988) 360-376.
2. Y. Huang, Vertex operator algebras and the Verlinde conjecture (2004); arXiv:math. QA/0406291.
3. J. Fuchs, Fusion rules in conformal field theory, Fortschr. Physik 42 (1994) 1-48; arXiv:hep-th/9306162.
4. D. Cox, J. Little and D. O'Shea, Ideals, Varieties, and Algorithms, Undergraduate Texts in Mathematics (Springer-Verlag, New York, 1992).
5. D. Gepner, Fusion rings and geometry, Comm. Math. Phys. 141 (1991) 381-411.
6. J. Polchinski, Dirichlet-branes and Ramond-Ramond charges, Phys. Rev. Lett. 75 (1995) 4724-4727; arXiv:hep-th/9510017.
7. R. Minasian and G. Moore, K-theory and Ramond-Ramond charge, JHEP 9711 (1997) 002; arXiv:hep-th/9710230.
8. P. Bouwknegt and D. Ridout, A note on the equality of algebraic and geometric D-brane charges in WZW models, JHEP 0405 (2004) 029; arXiv:hep-th/0312259.
9. S. Fredenhagen and V. Schomerus, Branes on group manifolds, gluon condensates, and twisted K-theory, JHEP 0104 (2001) 007; arXiv:hep-th/0012164.
10. P. Bouwknegt, P. Dawson and D. Ridout, D-branes on group manifolds and fusion rings, JHEP 0212 (2002) 065; arXiv:hep-th/0210302.
11. A. Tsuchiya, K. Ueno and Y. Yamada, Conformal field theories on universal families of stable curves with gauge symmetries, in lntegrable Systems in Quantum Field Theory and Statistical Mechanics, eds. M. Jimbo, T. Miwa and A. Tsuchiya (Academic Press, Boston, 1989), pp. 459-566.
12. G. Faltings, A proof for the Verlinde formula, J. Alg. Geom. 3 (1994) 347-374.
13. A. Beauville, Conformal blocks, fusion rules and the Verlinde formula, Israel Math. Conf. Proc. 9 (1996) 75-96; arXiv:alg-geom/9405001.
14. V. Kac and D. Peterson, Infinite-dimensional Lie algebras, theta functions and modular forms. Adv. Math. 53 (1984) 125-264.
15. V. Kac, Infinite Dimensional Lie Algebras: An Introduction (Birkhauser, Boston, 1983).
16. M. Walton, Fusion rules in Wess-Zumino-Witten models, Nucl. Phys. B 340 (1990) 777-790.
17. M. Walton, Algorithm for WZW fusion rules: A proof, Phys. Lett. B 241 (1990) 365-368.
18. J. Fuchs and P. van Driel, WZW fusion rules, quantum groups, and the modular matrix S, Nucl. Phys. B 346 (1990) 632-648.
19. P. Furlan, A. Ch. Ganchev and V. Petkova, Quantum groups and fusion rules multiplicities, Nucl. Phys. B 343 (1990) 205-227.
20. K fusion rings, Mod. Phys. Lett. A 7 (1992) 689-700; arXiv:hep-th/9111020.
21. D. Gepner and A. Schwimmer, Symplectic fusion rings and their metric, Nucl. Phys. B 380 (1992) 147-167; arXiv:hep-th/9204020.
22. k, and handle squashing, Nucl. Phys. B 393 (1993) 361-376; arXiv:hep-th/9110063.
23. E. Mlawer, H. Riggs and H. Schnitzer, Integrable N = 2 Landau-Ginzburg theories from quotients of fusion rings, Nucl. Phys. B 418 (1994) 603-636: arXiv:hep-th/9310082.
24. D. Ridout, D-brane charge groups and fusion rings in Wess-Zumino-Witten models, Ph.D. thesis. University of Adelaide (2005).
25. H. Weyl, The Classical Groups (Princeton University Press, Princeton, 1939).
26. N. Bourbaki, Lie Groups and Lie Algebras, Chapters 4-6 (Springer-Verlag, Berlin, 2002).
27. W. Fulton and J. Harris, Representation Theory: A First Course (Springer-Verlag, New York, 1991).
28. O. Aharony, Generalized fusion potentials, Phys. Lett. B 306 (1993) 276-282; arXiv:hep-th/9301118.
29. D. Cox, J. Little and D. O'Shea, Using Algebraic Geometry (Springer, New York, 1998).
30. J. Milnor, Singular Points of Complex Hyper-surfaces (Princeton University Press, Princeton, 1968).
31. A. Boysal and S. Kumar, Private communication (2005).
32. V. Braun, Twisted K-theory of Lie groups, JHEP 0403 (2004) 029; arXiv:hep-th/0305178.
33. M. Gaberdiel and T. Gannon, The charges of a twisted brane, JHEP 0401 (2004) 018; arXiv:hep-th/0311242.