  The Kapustin-Witten equations on R^4 are equations for a pair of connection
on the product principle SU(2) bundle and 1-form with values in the product Lie
algebra bundle. The 1-form is the Higgs field. A dichotomy is proved to the
effect that either the averaged norm of the Higgs field on large radius spheres
grows faster than a power of the radius, or its 1-form components everywhere
pairwise commute.
