Boundary conformal field theories on random surfaces and the non-critical open string

TL;DR

This paper studies boundary conformal field theories on random surfaces within the non-critical open string framework, focusing on boundary conditions of the Liouville field and their implications for string theory and gravitational scaling.

Contribution

It introduces a detailed analysis of boundary conditions on the Liouville field in non-critical open strings, including the semi-classical limit and new critical exponents.

Findings

Weyl anomaly cancellation conditions for various boundary conditions

Discontinuous metric behavior under Dirichlet boundary conditions

Definition of open string susceptibility and new critical exponents

Abstract

We analyse boundary conformal field theories on random surfaces using the conformal gauge approach of David, Distler and Kawai. The crucial point is the choice of boundary conditions on the Liouville field. We discuss the Weyl anomaly cancellation for Polyakov`s non-critical open bosonic string with Neumann, Dirichlet and free boundary conditions. Dirichlet boundary conditions on the Liouville field imply that the metric is discontinuous as the boundary is approached. We consider the semi-classical limit and argue how it singles out the free boundary conditions on the Liouville field. We define the open string susceptibility, the anomalous gravitational scaling dimensions and a new Yang-Mills Feynman mass critical exponent.