Rational links and DT invariants of quivers

TL;DR

This paper establishes a deep connection between rational links' colored HOMFLY-PT polynomials and motivic Donaldson-Thomas invariants of associated quivers, confirming conjectures and extending the links-quivers correspondence.

Contribution

It proves the links-quivers correspondence and LMOV conjecture for rational links, and extends the framework to tangles and skein theory for motivic DT invariants.

Findings

Colored HOMFLY-PT polynomials are specializations of motivic DT invariants.

Confirms the links-quivers correspondence for rational links.

Extends the correspondence to tangles and skein theory.

Abstract

We prove that the generating functions for the colored HOMFLY-PT polynomials of rational links are specializations of the generating functions of the motivic Donaldson-Thomas invariants of appropriate quivers that we naturally associate with these links. This shows that the conjectural links-quivers correspondence of Kucharski-Reineke-Sto\v{s}i\'c-Su{\l}kowski as well as the LMOV conjecture hold for rational links. Along the way, we extend the links-quivers correspondence to tangles and, thus, explore elements of a skein theory for motivic Donaldson-Thomas invariants.