  We show that the refined analytic torsion is a holomorphic section of the
determinant line bundle over the space of complex representations of the
fundamental group of a closed oriented odd dimensional manifold. Further, we
calculate the ratio of the refined analytic torsion and the Farber-Turaev
combinatorial torsion.
  As an application, we establish a formula relating the eta-invariant and the
phase of the Farber-Turaev torsion, which extends a theorem of Farber and
earlier results of ours. This formula allows to study the spectral flow using
methods of combinatorial topology.
