No-instanton conjecture for Vafa–Witten theory on 3-manifolds

Let $M_3$ be a 3-manifold and let $\mathcal{H}_{\mathrm{VW}}(M_3)$ denote the Vafa–Witten homology associated with it. No-instanton conjecture. In Vafa–Witten theory on 3-manifolds, there are no disk instantons contributing to $\mathcal{H}_{\mathrm{VW}}(M_3)$. The source supports this expectation using the absence of disk instantons in the associated sigma-model and the relation to an amphicheiral twist known to have no instantons; it does not state that the conjecture has been proved.