The fixed-point conjecture for Coulomb branches

Let $\mathcal M(\lambda,\mu)$ be the Coulomb branch associated with a quiver gauge theory, let $\chi\colon\mathbb C^\times\to\pi_1(\mathbf G)^\wedge$ be the one-parameter subgroup induced by a character of $\mathbf G$, and let $\mathcal M(\lambda,\mu)^\chi$ denote its fixed-point set. The fixed-point conjecture. The fixed-point set $\mathcal M(\lambda,\mu)^\chi$ is either empty or consists of a single point. This is proved for finite-type quivers and affine quivers of type $A$, while the general Kac–Moody case remains conjectural.