A study of non-critical strings in arbitrary dimensions

Abstract

A new classical action for two-dimensional gravity is established where the graviton is accompanied by a scalar partner, a dilaton. It is shown that the role of the dilaton field is to pacify the induced Liouville action, and to make quantum gravity easy to handle. The effective action, defined as the sum of the contributions from classical gravity, the ghosts, the induced Liouville mode and the matter, is a conformal theory. It is shown that this effective action can be interpreted as a non-linear sigma model, coupled to a linear dilaton background, in a target manifold with two additional fields and minkowskian signature. This helps us to identify the spectrum of non-critical strings in arbitrary dimensions. The analogous analysis of non-critical superstrings is also performed.