Annulus amplitude of FZZT branes revisited

TL;DR

This paper reexamines the annulus amplitude of FZZT branes across various matter sectors using matrix models and minimal Liouville gravity, confirming their consistency and decomposition into (1,1)-branes.

Contribution

It provides a unified analysis of FZZT brane amplitudes in different matter sectors, demonstrating agreement between matrix model and Liouville gravity approaches.

Findings

Confirmed the decomposition of FZZT branes into (1,1)-branes.

Established consistency between matrix model and Liouville gravity results.

Validated the boundary description of the 1-matrix model.

Abstract

We revisit the annulus amplitude of FZZT branes with general matter sectors (r,s) using the recent development of matrix model and minimal Liouville gravity. Following the boundary description of the 1-matrix model and bulk resonance transformation between primary operators we find the consistency of the brane decomposition into (1,1)-branes. We also investigate the corresponding results obtained directly from the minimal Liouville gravity and demonstrate the perfect agreement with the matrix results.