TWO DIMENSIONAL QUANTUM GRAVITY AND STRINGS

Abstract

We discuss some recent suggestions about a relation between 2-d quantum gravity and string theory. We consider the general 2-d σ model with D-dimensional target space coupled to 2-d quantum gravity and give arguments in favor of the conjecture that the effective theory which describes this system in the conformal gauge may be interpreted as a a model with a D+1-dimensional target space with the conformal factor of the metric playing the role of the D+1 coordinate. The latter σ model must be Weyl invariant while the original one may be arbitrary. The conformal “split” invariance which must be present in the conformal gauge imposes no restrictions on the original σ model couplings, but restricts the additional (D+1-dimensional) couplings which appear in the D+1-dimensional σ model.