Are there four-dimensional small black rings?

In $d>4$ dimensions, one can argue for the existence of small black rings using a scaling argument. We apply the same scaling argument to the $d=4$ case and demonstrate that it fails to say anything about the existence of $d=4$ small black rings, because stringy corrections get out of control. General relativity theorems say that there does not exist a black hole with toroidal topology for $d=4$, but we interpret this as saying that, for $d=4$ small black rings, stringy corrections are crucial which invalidate the assumptions those theorems are based on.