On Decay of K-theory

TL;DR

This paper explores how closed string tachyon condensation resolves orbifold singularities, affecting D-brane charges, and proposes a mathematical framework linking topology changes to a quantum version of the McKay correspondence.

Contribution

It introduces a gauged linear sigma model approach to track topology and D-brane charge changes during orbifold resolution, suggesting a quantum McKay correspondence.

Findings

Tachyon condensation reduces D-brane charges in orbifold resolutions.

Gauged linear sigma models effectively describe topology transitions.

Results suggest a new mathematical framework for singularity resolution.

Abstract

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.