Renormalization of the bilocal sine-Gordon model

The functional renormalization group treatment is presented for the two-dimensional sine-Gordon model including a bilocal term in the potential, which contributes to the flow at the tree level. It is shown that the flow of the bilocal term can substitute the evolution of the wave function renormalization constant, since it can recover the Kosterlitz-Thouless type phase transition. The flows can also reveal the connection between the sine-Gordon and the noninteracting Thirring models at a special value of the wave number parameter.