On the BPS spectrum of 5d SU(2) super-Yang-Mills

Abstract

We provide a closed-form expression for the motivic Kontsevich-Soibelman invariant for M-theory in the background of the toric Calabi-Yau threefold $K_{{\mathbb{F}}_0}$. This encodes the refined BPS spectrum of $SU(2)$ 5d $\mathcal{N}=1$ Yang-Mills theory on $S^1\times {\mathbb{R}}^4$, corresponding to rank-zero Donaldson-Thomas invariants for $K_{{\mathbb{F}}_0}$, anywhere on the Coulomb branch.

8 pages; v2 some updates due to an implicit assumption; v3 added appendix with proof of assumption, and some clarifications

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• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• TBA equations and quantum periods for D-type Argyres-Douglas theories
• Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers