Boundary Liouville theory at c=1

TL;DR

This paper extends the analysis of c=1 Liouville theory to boundary conditions, revealing a new family of boundary theories with band-gap spectra and providing explicit formulas for correlation functions.

Contribution

It introduces a new one-parameter family of boundary theories at c=1 derived from FZZT branes, with explicit correlation function formulas and geometric interpretations.

Findings

New boundary theories at c=1 with band-gap spectra

Explicit formulas for boundary 2-point functions

Geometric interpretation of ZZ and FZZT branes

Abstract

The c=1 Liouville theory has received some attention recently as the Euclidean version of an exact rolling tachyon background. In an earlier paper it was shown that the bulk theory can be identified with the interacting c=1 limit of unitary minimal models. Here we extend the analysis of the c=1-limit to the boundary problem. Most importantly, we show that the FZZT branes of Liouville theory give rise to a new 1-parameter family of boundary theories at c=1. These models share many features with the boundary Sine-Gordon theory, in particular they possess an open string spectrum with band-gaps of finite width. We propose explicit formulas for the boundary 2-point function and for the bulk-boundary operator product expansion in the c=1 boundary Liouville model. As a by-product of our analysis we also provide a nice geometric interpretation for ZZ branes and their relation with FZZT branes in the c=1 theory.