Anomaly-free vector perturbations with holonomy corrections in loop
  quantum cosmology
  We investigate vector perturbations with holonomy corrections in the
framework of loop quantum cosmology. Conditions to achieve anomaly freedom for
these perturbations are found at all orders. This requires the introduction of
counter-terms in the hamiltonian constraint. We also show that anomaly freedom
requires the diffeomorphism constraint to hold its classical form when scalar
matter is added although the issue of a vector matter source, required for full
consistency, remains to be investigated. The gauge-invariant variable and the
corresponding equation of motion are derived. The propagation of vector modes
through the bounce is finally discussed.
