  Lorentzian continuation of the Sine-Liouville model describes non-homogeneous
rolling closed string tachyon. Via T-duality, this relates to the gauged
$H_+^3$ Wess-Zumino-Witten model at subcritical level. This model is exactly
solvable. We give a closed formula for the 3-point correlation functions for
the model at level k within the range 0<k<2, which relates to the analogous
quantity for k>2 in a similar way as how the Harlow-Maltz-Witten 3-point
function of timelike Liouville field theory relates to the analytic
continuation of the Dorn-Otto-Zamolodchikov-Zamolodchikov structure constants:
We find that the ratio between both 3-point functions can be written in terms
of the Jacobi's $\theta $-function, while their product exhibits remarkable
cancellations and eventually factorizes. Our formula is consistent with
previous proposals made in the literature.
