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

TL;DR

This paper derives a closed-form expression for the motivic Kontsevich-Soibelman invariant, revealing the refined BPS spectrum of 5d SU(2) super-Yang-Mills theory on a specific background, applicable across the Coulomb branch.

Contribution

It provides the first explicit formula for the motivic invariant encoding the BPS spectrum of 5d SU(2) super-Yang-Mills theory on a toric Calabi-Yau background.

Findings

Closed-form expression for the motivic Kontsevich-Soibelman invariant.

Refined BPS spectrum characterized for 5d SU(2) theory.

Applicable to the Coulomb branch of the theory.

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 ${\cal N}=1$ 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.