A Note on the $c=1$ Barrier in Liouville Theory

TL;DR

This paper investigates the persistent instability of Liouville theory when coupled with matter fields exceeding central charge one, emphasizing that allowing interactions among singular geometries does not resolve the issue.

Contribution

It demonstrates that the instability in Liouville theory at $c>1$ remains even with interactions among spike-like geometries, clarifying the limitations of such models.

Findings

Instability persists for $c>1$ in Liouville theory.

Interactions among singular geometries do not stabilize the theory.

Highlights fundamental challenges in extending Liouville theory beyond $c=1$.

Abstract

The instability of Liouville theory coupled to $c>1$ matter fields is shown to persist even when the ``spikes'' which represent highly singular geometries are allowed to interact in a natural way.