Erratum: The holonomy of the determinant of cohomology of an algebraic bundle (Q5940531)

Let \(f:X \to Y\) be a smooth map between projective complex manifolds. Let \(E\) be a vector bundle on \(X\). There exists a connection associated to the Quillen metric on the determinant line bundle det\(Rf_*(E)\). In the original paper, the authors had done computations of the holonomy of this connection [\textit{H. Gillet} and \textit{C. Soulé}, Commun. Math. Phys. 131, 219-220 (1990; Zbl 0731.14030)]. Bismut has pointed out an error in those computations. The holonomy of the connection is a limit of certain terms as \(\varepsilon \to 0\). The authors had incorrectly claimed that these terms are independent of \(\varepsilon\). A counter example to the claim is also given.