BPS states, knots, and quivers

Abstract

The authors conjecture and test for several cases a new duality between knot invariants and quiver representations. Knot invariants supposedly capture the degeneracy of BPS states (Ooguri-Vafa invariants) in certain string theories, which are, according to this new conjecture, related to quiver moduli invariants, and are automatically integers. The latter would prove a long standing conjecture about Ooguri-Vafa invariants.