Pohozaev identities and bubbling obstruction for Yang-Mills fields in conformal dimension

Abstract

We study bubbling for sequences of Yang-Mills connections on closed four-manifolds and we derive a compatibility of Pohozaev type between the weak limit connection and the bubble formed at a concentration point, involving the Weyl tensor of the background metric. This yields obstruCtions to bubbling extending earlier results of Yin beyond the locally conformally flat case. As an application, we rule out certain bubbling configurations on CP2.