A local induced action for the noncritical string

Abstract

We present an alternative to Polyakov’s induced action for the noncritical string. Our Yang–Mills-like action is both local and invariant under coordinate transformations. It defines a teleparallel theory of gravity with interesting links to Hořava–Lifshitz and Einstein-aether theories. It is of Liouville type in the conformal gauge, while, remarkably, in the proper-time gauge, it gives an effective action familiar from the causal dynamical triangulation approach to 2D quantum gravity. In the latter gauge the effective action is especially interesting since its quantization is known to reduce to a quantum mechanical model.