Vanishing conjecture for compact anti-self-dual Einstein 4-manifolds

Let $(M^{4},g)$ be a compact anti-self-dual Einstein manifold with negative scalar curvature. Anti-self-dual Einstein vanishing conjecture. All the Seiberg–Witten invariants vanish for the fixed orientation of $M$. Real- and complex-hyperbolic $4$-manifolds provide special cases because they are Einstein, while the relevant orientation makes complex-hyperbolic manifolds anti-self-dual. The conjecture is stated as a generalization of the preceding speculations and is presented as open.