Collins's chiral-ring K-stability conjecture

Let $(X,\zeta)$ be a polarized ring with symmetry or Reeb vector field $\zeta$. The ring is the chiral ring of a four-dimensional $\mathcal{N}=1$ superconformal field theory (SCFT) when it is the ring of operators annihilated by $\widehat{Q_{\dot{\alpha}}}$, modulo operators of the form $\{\widehat{Q_{\dot{\alpha}}},\_\}$. Collins's chiral-ring K-stability conjecture. The ring $(X,\zeta)$ is the chiral ring of an SCFT if and only if $X$ is K-stable. This conjecture proposes K-stability as the criterion for a polarized ring to arise as the chiral ring of an SCFT; the source gives no resolution status.