标题： FZZT膜的环形幅值的重新研究 显示英文标题

标题： Annulus amplitude of FZZT branes revisited

摘要： 我们重新研究了具有一般物质部分(r,s)的FZZT膜的环面振幅，利用矩阵模型和最小Liouville引力的最新发展。根据1矩阵模型的边界描述和原初算符之间的体共振变换，我们发现膜分解为(1,1)-膜的一致性。我们还研究了直接从最小Liouville引力得到的相应结果，并证明与矩阵结果完全一致。 显示英文摘要

摘要： 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.