Quantum McKay correspondence for disc invariants of orbifold vertex

TL;DR

This paper presents a systematic method for resolving orbifold vertices torically and demonstrates the equivalence of disc invariants between orbifold vertices and their crepant resolutions.

Contribution

It introduces a procedure to find toric crepant resolutions and links disc invariants of orbifold vertices to those of their resolutions.

Findings

Disc invariants of orbifold vertices match those of their toric crepant resolutions.

Provides a systematic approach for resolving orbifold vertices torically.

Establishes a correspondence between generating series of disc invariants.

Abstract

In this note, we describe a a systematic procedure to find toric crepant resolutions of orbifold vertex, and show that the generating series of certain disc invariants of the orbifold vertex can be suitably identified with the generating series of certain disc invariants of its toric crepant resolutions.