Euclidean counterpart of the SL($2,\mathbb R$)-WZNW model, by analytic continuation. However, more care must be taken when dealing with amplitudes involving spectral flowed insertions. There are two known strategies for computing these correlation functions, both exploiting the singular properties of the so-called spectral flow operator.

Regarding the first one, the computation is performed in the original space-time picture. Roughly speaking, every vertex operator associated with a state carrying a single unit of spectral flow is expressed as an unflowed vertex convoluted with a spectral flow operator, the corresponding integral being understood to hold while inside a correlator. This integral definition was introduced and subsequently used for determining the regular term of the propagator of two $\omega=1$ states and the three-point function involving two spectrally unflowed states and one vertex with unit spectral flow in [@Maldacena:2001km]. The main restraint of the procedure comes from the fact that the referred integral definition of a spectral flowed vertex exists, so far, only for operators with a single unit of spectral flow. The generalization for an arbitrary charge of spectral flow is still lacking.

The second strategy is the so-called FZZ procedure. It was firstly developed in [@Fateev] based on parafermionic operators and the 