Regularity and vanishing theorems for Yang-Mills-Higgs pairs (Q2414681)

The purpose of the present paper is to establish vanishing and regularity theorems for Yang-Mills-Higgs pairs on Riemannian spaces of dimension \(n>4\). Such results are known to hold for Yang-Mills fields and harmonic maps. The author shows that they carry over naturally to solutions to the Yang-Mills-Higgs system, which is in some sense a coupling of the Yang-Mills and harmonic map systems. Moreover, the regularity theorem is used to establish a partial compactness theorem. Along the way, the author investigates the monotonicity and scaling properties of such pairs, obtaining a generalization of the well-known monotonicity formula for Yang-Mills connections.