Quiver diagonalization and open BPS states

Abstract

We show that motivic Donaldson-Thomas invariants of a~symmetric quiver $Q$, captured by the generating function $P_Q$, can be encoded in another quiver $Q^{(\infty )}$ of (almost always) infinite size, whose only arrows are loops, and whose generating function $P_{Q^{(\infty )}}$ is equal to $P_Q$ upon appropriate identification of generating parameters. Consequences of this statement include a generalization of the proof of integrality of Donaldson-Thomas and Labastida-Mariño-Ooguri-Vafa invariants that count open BPS states, as well as expressing motivic Donaldson-Thomas invariants of an arbitrary symmetric quiver in terms of invariants of $m$-loop quivers. In particular, this means that the already known combinatorial interpretation of invariants of $m$-loop quivers extends to arbitrary symmetric quivers.

arXiv comment37 pages

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