The charges of a twisted brane
Matthias R Gaberdiel, Terry Gannon
TL;DR
This paper determines the charges of twisted D-branes in specific WZW models, showing they are labeled by twisted representations and have a charge group isomorphic to that of untwisted branes, confirmed through Lie algebra identities.
Contribution
It provides a detailed calculation of twisted D-brane charges and proves their charge group matches that of untwisted branes, aligning with K-theory predictions.
Findings
Twisted D-brane charges are given by ground state multiplicities.
The charge group of twisted branes is isomorphic to that of untwisted branes.
The proof involves non-trivial Lie algebra identities.
Abstract
The charges of the twisted D-branes of certain WZW models are determined. The twisted D-branes are labelled by twisted representations of the affine algebra, and their charge is simply the ground state multiplicity of the twisted representation. It is shown that the resulting charge group is isomorphic to the charge group of the untwisted branes, as had been anticipated from a K-theory calculation. Our arguments rely on a number of non-trivial Lie theoretic identities.
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