Brief comments on Jackiw-Teitelboim gravity coupled to Liouville theory

Jackiw-Teitelboim gravity with non-vanishing cosmological constant coupled to Liouville theory is considered as a non-critical string on $d$ dimensional flat spacetime. It is discussed how the presence of cosmological constant yields additional constraints on the parameter space of the theory, even when the conformal anomaly is independent of the cosmological constant. Such constraints agree with the necessary conditions for the tachyon field to be a primary --prelogarithmic-- operator of the worldsheet 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 free field prescription leads to obtain explicit expressions for three-point correlation functions for the case of vanishing cosmological constant in terms of a product of Shapiro-Virasoro integrals. This is a consequence of the mentioned neutralization effect.Comment: 14 pages, no figures. v2 References added. To be published in Classical and Quantum Gravity. v3 typos correcte