Charges of twisted branes: the exceptional cases

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  1. A similar proposal was made in [21] based on an analysis for large level.

  2. For the case of \(D_4\), there are in total five ‘twisted’ classes of branes that are associated to \(\omega\), \(\omega^2\), \(C\), \(\omega C\) and \(\omega^2 C\), where \(C\) denotes charge conjugation. The corresponding NIM-reps are all closely related to the one discussed in this paper, or the charge conjugation NIM-rep discussed in [13] (see [16]). The arguments given here, together with the results of [13] therefore imply that these five twisted classes of D-branes account for five summands in (1.1).

  3. This relation was already noted in [16].

  4. Note that the charge constraint (2.2) as well as the expression (2.13) for the NIM-rep is valid also for highest weights \(\lambda\) which are not in \(\mathcal{P}_{k}^{+} (D_{4})\).