  The worldvolume theory of coincident M5-branes is expected to contain a
nonabelian 2-form/nonabelian gerbe gauge theory that is a higher analog of
self-dual Yang-Mills theory. But the precise details -- in particular the
global moduli / instanton / magnetic charge structure -- have remained elusive.
Here we deduce from anomaly cancellation a natural candidate for the
holographic dual of this nonabelian 2-form field, under AdS7/CFT6-duality. We
find this way a 7-dimensional nonabelian Chern-Simons theory of String
2-connection fields, which, in a certain higher gauge, are given locally by
non-abelian 2-forms with values in an affine Kac-Moody Lie algebra. We
construct the corresponding action functional on the entire smooth moduli
2-stack of field configurations, thereby defining the theory globally, at all
levels and with the full instanton structure, which is nontrivial due to the
twists imposed by the quantum corrections. Along the way we explain some
general phenomena of higher nonabelian gauge theory that we need.
