Abstract
The affine Kac-Moody algebras give rise to rational conformal field theories (RCFTs) called the Wess-Zumino-Witten (WZW) models. An important component of an RCFT is its fusion ring, whose structure constants are given by the associated S-matrix. We apply a fixed point property possessed by the WZW models ("fixed point factorization") to calculate nonnegative integer matrix representations of the fusion ring, allowing for the calculation of D-brane charges in string theory.
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