Non-Perturbative Formulation of Non-Critical String Models

TL;DR

This paper introduces a non-perturbative renormalization-group approach to non-critical bosonic Liouville string models, revealing a fixed point where the target space-time becomes Minkowski and the Liouville field's dynamics are trivial, supporting its identification with target time.

Contribution

It presents a novel non-perturbative renormalization-group technique applied to non-critical string models, demonstrating a fixed point with Minkowski space-time and trivial Liouville dynamics.

Findings

Existence of a renormalization-group fixed point as Q approaches 0.

Target space-time becomes Minkowski at the fixed point.

Liouville field's zero mode can be identified with target time, up to a minus sign.

Abstract

We apply to non-critical bosonic Liouville string models, characterized by a central-charge deficit Q, a new non-perturbative renormalization-group technique based on a functional method for controlling the quantum fluctuations. We demonstrate the existence of a renormalization-group fixed point of Liouville string theory as Q to 0, in which limit the target space-time is Minkowski and the dynamics of the Liouville field is trivial, as it neither propagates nor interacts. This calculation supports in a non-trival manner the identification of the zero mode of the Liouville field with the target time variable, up to a crucial minus sign.