Non critical super strings on world sheets of constant curvature

We consider correlation functions in Neveu--Schwarz string theory coupled to two dimensional gravity. The action for the 2D gravity consists of the string induced Liouville action and the Jackiw--Teitelboim action describing pure 2D gravity. Then gravitational dressed dimensions of vertex operators are equal to their bare conformal dimensions. There are two possible interpretations of the model. Considering the 2D dilaton and the Liouville field as additional target space coordinates one gets a $d+2$-dimensional critical string. In the $d$-dimensional non critical string picture gravitational fields retain their original meaning and for $d=4$ one can get a mass spectrum via consistency requirements. In both cases a GSO projection is possible.