Growth of the Higgs field for solutions to the Kapustin-Witten equations on R^4
arXiv:1701.03072
Abstract
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.