String theory landscape and cosmological constant

Abstract

In this paper we considered the bosonic string action in the presence of metric $G_{\mu\nu}$, Kalb-Ramond field $B_{\mu\nu}$ and dilaton field $\Phi$. The quantum conformal invariance is achieved if all three one-loop $\beta$-functions are zero. But, $\beta^\Phi$, $\beta$-function related to the dilaton field, can also be equal to some nonzero constant $c$, which is actually the central charge of Virasoro algebra. The anomaly contained in the Schwinger term of Virasoro algebra is canceled by adding Liouville term to the sigma model action and quantum conformal invariance is restored. The space-time action, which Euler-Lagrange equations of motion are quantum conformal invariance conditions with nonzero $\beta^{\Phi}$, is Einstein-Hilbert action with some matter and cosmological constant. The cosmological constant is obtained within landscape framework as linear function of the central charge of Virasoro algebra.