A local induced action for the noncritical string

TL;DR

This paper introduces a local, coordinate-invariant action for noncritical strings that connects teleparallel gravity with quantum gravity approaches like CDT, offering new insights into 2D quantum gravity.

Contribution

It proposes a novel local induced action for noncritical strings, linking teleparallel gravity to established quantum gravity frameworks and providing a new gauge perspective.

Findings

The action is local and invariant under coordinate transformations.

In the proper-time gauge, the effective action aligns with CDT models.

Quantization reduces to a quantum mechanical model in the proper-time gauge.

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 Horava-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 (CDT) 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.