Boundary conditions in charge conjugate sl(N) WZW theories
Abstract
Description
We compute the representations (``nimreps'') of the fusion algebra of affine sl(N), which determine the boundary conditions of sl(N) WZW theories twisted by the charge conjugation. This is done following two procedures, one of general validity, the other specific to the problem at hand. The problem is related to the classical problem of decomposition of the fundamental representations of sl(N) onto representations of $B_l=so(2l+1)$ or $C_l =sp(2l)$ algebras. The relevant nimreps and their diagonalisation matrix are thus expressed in terms of modular data of the affine B or C algebras
19 pages, harvmac.tex, 1 figure; v4: misprints corrected, the Note added comparing with hep-th/9905038 expanded. A summary of the results of the paper is published in the Proceedings of the NATO Advanced Research Workshop, {\bf Statistical Field Theories}, Como, 2001, eds. A. Cappelli and G. Mussardo, Kluwer Academic Publishers, 2002, p. 161-170
19 pages, harvmac.tex, 1 figure; v4: misprints corrected, the Note added comparing with hep-th/9905038 expanded. A summary of the results of the paper is published in the Proceedings of the NATO Advanced Research Workshop, {\bf Statistical Field Theories}, Como, 2001, eds. A. Cappelli and G. Mussardo, Kluwer Academic Publishers, 2002, p. 161-170