On Decay of K-theory

Closed string tachyon condensation resolves the singularities of nonsupersymmetric orbifolds, however the resolved space typically has fewer D-brane charges than that of the orbifold. The description of the tachyon condensation process via a gauged linear sigma model enables one to track the topology as one passes from the sigma model's ``orbifold phase'' to its resolved, ``geometric phase,'' and thus to follow how the D-brane charges disappear from the effective spacetime dynamics. As a mathematical consequence, our results point the way to a formulation of a ``quantum McKay correspondence'' for the resolution of toric orbifold singularities.