Transgression of the index gerbe

Abstract

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 $LB$.