String theory landscape and cosmological constant

In this letter we considered the bosonic string action in the presence of metric $G_{\mu\nu}$, Kalb-Ramond field $B_{\mu\nu}$ and dilaton field $\Phi$. We commented the conditions for quantum conformal invariance using standard approach (all three $\beta$ functions are zero) and the second one, adding Liouville term to the sigma model action. Analyzing the second one and writing down the effective action, we get Einstein-Hilbert action with some matter and cosmological constant, which is expressed in terms of the central charge of Virasoro algebra. The fact that string theory landscape produces cosmological constant is a little bit unexpected result. It is also interesting that we, for one special choice of background fields, after rescalling space-time metric, made a possible connection to the Conformal Cyclic Cosmology (CCC). It turns out that cosmological constant is conserved in the period of the succession of aeons, which could mean that one aeon inherits the inflationary expansion from the previous one.