Brief comments on Jackiw-Teitelboim gravity coupled to Liouville theory

The Jackiw-Teitelboim gravity with non-vanishing cosmological constant coupled to Liouville theory is considered as a non-critical string on d dimensional Minkowski space-time. It is discussed how the presence of cosmological constant leads to consider additional constraints on the parameters of the theory, even though the conformal anomaly is idependent of the cosmological constant. The constraints agree with the conditions necessary to ensure that the tachyon field turns out to be a primary prelogarithmic operator within the context of the world-sheet conformal field theory. Thus, the linearized tachyon field equation allows to impose the diagonal condition for the interaction term. We analyze the neutralization of the Liouville mode induced by the coupling to the Jackiw-Teitelboim lagrangian. The standard free field prescription leads to obtain explicit expressions for three-point functions for the case of vanishing cosmological constant in terms of a product of Shapiro-Virasoro integrals; this fact is a consequence of the mentioned neutralization effect.