RATIONAL MAPS, MONOPOLES AND SKYRMIONS

We discuss the similarities between BPS monopoles and skyrmions, and p oint to an underlying connection in terms of rational maps between Rie mann spheres. This involves the introduction of a new ansatz for Skyrm e fields. We use this to construct good approximations to several know n skyrmions, including all the minimal energy configurations up to bar yon number nine, and some new solutions such as a baryon number sevent een Skyrme field with the truncated icosahedron structure of a buckyba ll. The new approach is also used to understand the low-lying vibratio nal modes of skyrmions, which are required for quantization. Along the way we discover an interesting Morse function on the space of rationa l maps which may be of use in understanding the Sen forms on the monop ole moduli spaces. (C) 1998 Published by Elsevier Science B.V.