  We consider the first order formalism in string theory, providing a new
off-shell description of the nontrivial backgrounds around an "infinite
metric". The OPE of the vertex operators, corresponding to the background
fields in some "twistor representation", and conditions of conformal invariance
results in the quadratic equation for the background fields, which appears to
be equivalent to the Einstein equations with a Kalb-Ramond B-field and a
dilaton. Using a new representation for the Einstein equations with B-field and
dilaton we find a new class of solutions including the plane waves for metric
(graviton) and the B-field. We discuss the properties of these background
equations and main features of the BRST operator in this approach.
