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The infrared problem of the effective action in 2D is discussed in theframework of the Covariant Perturbation Theory. The divergences are regularisedby a mass and the leading term is evaluated up to the third order ofperturbation theory. A summation scheme is proposed which isolates thedivergences from the finite part of the series and results in a single term.The latter turns out to be equivalent to the coupling to a certain classicalexternal field. This suggests a renormalisation by factorisation.Comment: 25 page

IR renormalization of general effective actions and Hawking flux in 2D gravity theories