The Vafa-Witten equations on an oriented Riemannian 4-manifold are first order, non-linear equations for a pair of connection on a principle SO(3) bundle over a 4-manifold and a self-dual 2-form with values in the associated Lie algebra bundle. This talk will describe a theorem about the behavior of sequences of solutions to the Vafa-Witten equations which have no convergent sub-sequence. This theorem says in part that a renormalization of a subsequence of the self-dual 2-form components of any given solution sequence converges on the complement of a closed set with Hausdorff dimension at most 2; and the limit defines a harmonic 2-form with values in a real line bundle.
Back to Gauge Theory and Categorification
Copyright. All Rights Reserved.