How can one derive Schwarzian derivative action as low energy effective field theory invariant under global $SL(2,\mathbb{R})$?

Question

In a recent paper (page 47, below eq (4.173)) they make a passing claim that the Schwarzian derivative action can be derived using effective low energy field theory reasoning. I imagine they mean that if I want to construct a least derivative action which is invariant under global $SL(2,\mathbb{R})$ transformations of the coordinates, then I will end up with Schwarzian derivative. I was wondering if this has been worked out anywhere. Also, using the same approach, what are the higher derivative invariants that I can possibly construct as 'less relevant' terms.

This post imported from StackExchange Physics at 2019-05-05 13:10 (UTC), posted by SE-user nGlacTOwnS