Non-critical $d=2$ Gravities and Integrable Models

TL;DR

This paper reviews the emergence of anomaly-driven dynamics in two-dimensional gravity theories, emphasizing the use of BRST symmetry and quantum canonical transformations to solve Liouville and Toda models for anomalous modes.

Contribution

It introduces a BRST-based perspective and demonstrates how quantum canonical transformations can solve integrable models in 2D gravity.

Findings

BRST framework clarifies anomaly-induced dynamics

Quantum canonical transformations solve Liouville/Toda models

Provides a unified approach to 2D gravity and integrable models

Abstract

We review the origin of anomaly-induced dynamics in theories of $d=2$ gravity from a BRST viewpoint and show how quantum canonical transformations may be used to solve the resulting Liouville or Toda models for the anomalous modes.