  Recently, for a family of ungraded Dirac operators over some space $B$ J.
Lott constructed an index gerbe. In the present paper we show (in analogy to
the holonomy formula for the determinant bundle in the graded case) that the
holonomy of the index gerbe (a priori a hermitean line bundle with connection
over the free loop space $LB$) coincides with an adiabatic limit of determinant
bundles of an associated family of graded Dirac operators over $LB$.

Differential Geometry