  Given a family of Dirac operators with vanishing spectral flow we construct a
thin-invariant rank-one field theory in the sense of Turner and Willerton
arXiv:math.AT/0201116. Our construction of the field theory generalizes the one
of the index gerbe by Lott, arXiv:math.DG/0106177, and it also complements the
relation between gerbes and thin-invariant rank-one field theories studied in
arXive:math.AT/0201116.
