Localized Tachyons and the Quantum McKay Correspondence

The condensation of closed string tachyons localized at the fixed point of aC^d/\Gamma orbifold can be studied in the framework of renormalization groupflow in a gauged linear sigma model. The evolution of the Higgs branch alongthe flow describes a resolution of singularities via the process of tachyoncondensation. The study of the fate of D-branes in this process has lead to anotion of a ``quantum McKay correspondence.'' This is a hypotheticalcorrespondence between fractional branes in an orbifold singularity in theultraviolet with the Coulomb and Higgs branch branes in the infrared. In thispaper we present some nontrivial evidence for this correspondence in the caseC^2/Z_n by relating the intersection form of fractional branes to that of``Higgs branch branes,'' the latter being branes which wrap nontrivial cyclesin the resolved space.Comment: 25 pages; harvma