Localized Tachyons and the Quantum McKay Correspondence

TL;DR

This paper investigates the process of localized tachyon condensation in orbifold singularities using gauged linear sigma models, proposing a quantum McKay correspondence relating fractional and Higgs branch branes.

Contribution

It provides evidence for a quantum McKay correspondence linking fractional branes to Higgs branch branes in C^2/Z_n orbifolds.

Findings

Intersection form of fractional branes matches that of Higgs branch branes.

Tachyon condensation leads to resolution of singularities.

Supports the quantum McKay correspondence hypothesis.

Abstract

The condensation of closed string tachyons localized at the fixed point of a C^d/\Gamma 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^2/Z_n 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.