The asymptotics of the analytic torsion on CR manifolds with S 1 action

Let X be a compact connected strongly pseudoconvex CR manifold of dimension 2n + 1, n ≥ 1 with a transversal CR S1-action on X. We introduce the Fourier components of the Ray-Singer analytic torsion on X with respect to the S1-action. We establish an asymptotic formula for the Fourier components of the analytic torsion with respect to the S1-action. This generalizes the asymptotic formula of Bismut and Vasserot on the holomorphic Ray-Singer torsion associated with high powers of a positive line bundle to strongly pseudoconvex CR manifolds with a transversal CR S1-action.