The reduction of the $E_8$ gauge theory to ten dimensions leads to a loop
group, which in relation to twisted $K$-theory has a Dixmier–Douady class
identified with the Neveu–Schwarz $H$-field. We give an interpretation of
the degree two part of the eta form by comparing the adiabatic limit of the
eta invariant with the one loop term in type IIA. More generally, starting
with a $G$-bundle, the comparison for manifolds with String structure
identifies $G$ with $E_8$ and the representation as the adjoint, due to an
interesting appearance of the dual Coxeter number. This makes possible
a description in terms of a generalized Wess-Zumino-Witten model at
the critical level. We also discuss the relation to the index gerbe, the
possibility of obtaining such bundles from loop space, and the symmetry
breaking to finite-dimensional bundles. We discuss the implications of
this and we give several proposals.