There is some link between Ricci-flatness and reduction of holonomy. For example a Kahler manifold is Ricci-flat if and only if it has at most $SU(n)$ holonomy rather than $U(n)$, and it's apparently open to construct a closed, simply-connected Ricci-flat manifold with full $SO(n)$ holonomy.

On a manifold with an arbitrary affine connection, the Ricci curvature still makes sense. By any chance, does being Ricci-flat imply a reduction of the holonomy? In particular, does it imply that the connection is compatible with some (pseudo-Riemannian) metric (i.e. that the holonomy is contained in some $O(p,q)$)? I'm happy to assume the connection is torsion-free. And I'm really most interested in the *local* holonomy, so assume the manifold is simply-connected if that makes a difference.

(The motivation for this question comes from thinking very naively about general relativity as a pure gauge theory, which I think makes sense in a vacuum at least. Maybe in this case the metric constraint comes for free!)