Non critical super strings on world sheets of constant curvature

TL;DR

This paper studies correlation functions in a non-critical superstring theory coupled with 2D gravity, revealing that gravitational dressing leaves vertex operator dimensions unchanged and exploring interpretations as higher-dimensional or non-critical strings.

Contribution

It introduces a model combining Liouville and Jackiw-Teitelboim actions, showing gravitational dressing does not alter vertex operator dimensions and discussing two interpretations of the theory.

Findings

Gravitational dressing preserves vertex operator dimensions.

Two interpretations: as a higher-dimensional critical string or a non-critical string with mass spectrum.

GSO projection is possible in both interpretations.

Abstract

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.