Finite deformations of CFT and space-time geometry

We demonstrate in detail how the space of 2D quantum field theories can be parameterized by off-shell states of free closed string. The dynamic equation corresponding to the condition of conformal invariance includes an infinite number of higher order terms, and we give an explicit procedure for their calculation. The symmetries corresponding to equivalence relations of CFT are described. In this framework we show how to perform nonperturbative analysis in the low-energy limit and prove that it corresponds to Brans-Dicke theory of gravity interacting with a skewsymmetric tensor field. (orig.)