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Jackiw-Teitelboim gravity with non-vanishing cosmological constant coupled toLiouville theory is considered as a non-critical string on $d$ dimensional flatspacetime. It is discussed how the presence of cosmological constant yieldsadditional constraints on the parameter space of the theory, even when theconformal anomaly is independent of the cosmological constant. Such constraintsagree with the necessary conditions for the tachyon field to be a primary--prelogarithmic-- operator of the worldsheet conformal field theory. Thus, thelinearized tachyon field equation allows to impose the diagonal condition forthe interaction term. We analyze the neutralization of the Liouville modeinduced by the coupling to the Jackiw-Teitelboim Lagrangian. The free fieldprescription leads to obtain explicit expressions for three-point correlationfunctions for the case of vanishing cosmological constant in terms of a productof Shapiro-Virasoro integrals. This is a consequence of the mentionedneutralization effect.Comment: 14 pages, no figures. v2 References added. To be published in  Classical and Quantum Gravity. v3 typos correcte

Brief comments on Jackiw–Teitelboim gravity coupled to Liouville theory