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arXiv · 1707.02991

BPS states, knots and quivers

Piotr Kucharski·Markus Reineke·Marko Stosic·Piotr Sułkowski
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Abstract

We argue how to identify 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-Mari\~no-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, conjectured originally based on string theory and M-theory arguments.

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Piotr Kucharski, Markus Reineke, Marko Stosic, Piotr Sułkowski. 2017-07-10. BPS states, knots and quivers. https://doi.org/10.1103/physrevd.96.121902

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