Boundary c≤1 Liouville CFT from the Bootstrap
Panos Betzios, Paul Ghiringhelli, Olga Papadoulaki, Ioannis Tsiares
Abstract
We construct boundary Liouville conformal field theory at central charge c≤1 with FZZT-type boundary conditions and show that it satisfies the Cardy--Lewellen sewing constraints on the disk and the annulus. Using the analytic bootstrap we derive the so far missing boundary three-point and bulk-to-boundary structure constants and a consistent disk one-point function as explicit meromorphic functions of the Liouville momenta. In sharp contrast to c≥25, the open-string spectrum between two ``timelike'' FZZT boundaries is discrete, yet non-trivially consistent through open-closed duality with the continuous closed-string spectrum of Ribault and Santachiara.
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