SKYRME CRYSTAL FROM A TWISTED INSTANTON ON A 4-TORUS

We describe how an approximation to the minimal energy Skyrme crystal can be obtained from the holonomy of a Yang-Mills instanton. The appro priate instanton is twisted on a four-torus and has instanton number e qual to one half. It generates a Skyrme field with the correct topolog ical and symmetry properties of the crystal. An explicit solution for the instanton is not known, but an analytical fit to numerical data is available and using this we obtain a Skyrme crystal whose energy is o nly 2% above that of the (numerically) known solution.