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].
Categories: math.DG