2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63224Given 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/0201116.9 pagesDifferential GeometryAlgebraic Topology58J28text