Kawai-Lewellen-Tye Relation, see here, is a perfect tool to make connections between amplitudes. The most general of them is the relation between a tree gravity amplitude (from Einstein-Hilbert action) and a gauge theory amplitude (from Yang-Mills). We can also relate the closed strings amplitude and open strings amplitude using KLT. (Many connections are there for closed strings algebra and open strings. From a conversation with Ed Witten; Ed - The simplest is that they can be computed in similar ways by integral representations that come from the open or closed string).

From the paper (recommended);

and same paper (sec II, a short review);

More papers on this subject; here, here, and here.