The Two-exponential Liouville Theory and the Uniqueness of the   Three-point Function
  It is shown that in the two-exponential version of Liouville theory the coefficients of the three-point functions of vertex operators can be determined uniquely using the translational invariance of the path integral measure and the self-consistency of the two-point functions. The result agrees with that obtained using conformal bootstrap methods. Reflection symmetry and a previously conjectured relationship between the dimensional parameters of the theory and the overall scale are derived. 
L. O'Raifeartaigh, J. M. Pawlowski, and V. V. Sreedhar