Yang-Mills Connections on Conformally Compact Manifolds

Abstract

We study the moduli space of Yang--Mills connections on bundles over a conformally compact manifold $\overline{M}$. We prove that, for every Yang--Mills connection $A$ that satisfies an appropriate nondegeneracy condition, and for every small deformation $\gamma$ of $A_{|\partial \overline{M}}$, there is a Yang--Mills connection in the interior that extends $A_{|\partial \overline{M}}+\gamma$. As a corollary, we confirm an expectation of Witten mentioned in his foundational paper about holography [arXiv:hep-th/9802150].

Replaced with fully revised version. The preliminary sections containing preliminary material have been reduced, and now contain only the background tools needed to prove the main theorem; the main theorem (Theorem 63) and its proof are essentially unchanged; Theorem 65 has been removed for the sake of brevity; Theorem 75 has been removed while I try and fix a gap in the proof

References in corpus (1)

• On the geometry of Riemannian manifolds with a Lie structure at infinity

Cited by in corpus (2)

• Biharmonic Maps Between Conformally Compact Manifolds
• E-structures and almost regular Poisson manifolds