Gravitational Yang–Lee model: Four-point function

We find the four-point perturbative contribution to the spherical partition function of the gravitational Yang–Lee model numerically. We propose an effective integration procedure based on a convenient elliptic parameterization of the moduli space. At certain values of the "spectator" parameter, the Liouville four-point function involves several "discrete terms," which should be taken into account separately. We also consider the classical limit, where only the discrete terms survive. In addition, we propose an explicit expression for the spherical partition function at the "second explicitly solvable point," where the spectator matter is yet another $\mathcal{M}_{2/5}$ (Yang–Lee) minimal model.