Localized Tachyons and the Quantum McKay Correspondence

The condensation of closed string tachyons localized at the fixed point of a C/Γ orbifold can be studied in the framework of renormalization group flow in a gauged linear sigma model. The evolution of the Higgs branch along the flow describes a resolution of singularities via the process of tachyon condensation. The study of the fate of D-branes in this process has lead to a notion of a “quantum McKay correspondence.” This is a hypothetical correspondence between fractional branes in an orbifold singularity in the ultraviolet with the Coulomb and Higgs branch branes in the infrared. In this paper we present some nontrivial evidence for this correspondence in the case C/ZZn by relating the intersection form of fractional branes to that of “Higgs branch branes,” the latter being branes which wrap nontrivial cycles in the resolved space.