Liouville D-branes in Two-Dimensional Strings and Open String Field Theory

TL;DR

This paper analyzes open strings on Liouville D-branes in the 2D bosonic string theory at the self-dual radius, deriving boundary correlators, regularizing divergences, and connecting to a matrix model for open-string field theory.

Contribution

It provides explicit boundary correlator formulas, introduces a regularization scheme for divergences, and links the open string field theory to a novel matrix model.

Findings

Boundary correlators depend only on differences of boundary cosmological constants.

Divergences at self-dual radius can be regularized and renormalized.

Open-string field theory relates to an interesting matrix model.

Abstract

We study open strings in the noncritical $c=1$ bosonic string theory compactified on a circle at self-dual radius. These strings live on D-branes that are extended along the Liouville direction ({\it FZZT} branes). We present explicit expressions for the disc two- and three-point functions of boundary operators in this theory, as well as the bulk-boundary two-point function. The expressions obtained are divergent because of resonant behaviour at self-dual radius. However, these can be regularised and renormalized in a precise way to get finite results. The boundary correlators are found to depend only on the differences of boundary cosmological constants, suggesting a fermionic behaviour. We initiate a study of the open-string field theory localised to the physical states, which leads to an interesting matrix model.