Authors: Kucharski, Piotr
Reineke, Markus
Stošić, Marko 
Sułkowski, Piotr
Title: BPS states, knots, and quivers
Journal: Physical Review D
Volume: 96
Issue: 12
Issue Date: 15-Dec-2017
Rank: M21
ISSN: 2470-0010
DOI: 10.1103/PhysRevD.96.121902
We argue how to identify the supersymmetric quiver quantum mechanics description of BPS states, which arise in string theory in brane systems representing knots. This leads to a surprising relation between knots and quivers: to a given knot, we associate a quiver, so that various types of knot invariants are expressed in terms of characteristics of a moduli space of representations of the corresponding quiver. This statement can be regarded as a novel type of categorification of knot invariants, and among its various consequences we find that Labastida-Mariño-Ooguri-Vafa (LMOV) invariants of a knot can be expressed in terms of motivic Donaldson-Thomas invariants of the corresponding quiver; this proves integrality of LMOV invariants (once the corresponding quiver is identified), conjectured originally based on string theory and M-theory arguments.
Publisher: American Physical Society
Project: Quantum fields and knot homologies 
Geometry, Education and Visualization With Applications 

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