# Boundary Liouville CFT
Boundary Liouville CFT is a [[0548 Boundary CFT|BCFT]] whose closed sector is [[0562 Liouville theory|Liouville CFT]]. Like the three-point function on the sphere, which is given by the DOZZ formula, the three-point function of boundary operators on the disk has also been derived.
Two special boundary conditions that are imposed on the boundary are [[0652 ZZ brane|ZZ branes]] and [[0658 FZZT brane|FZZT branes]].
## Refs
- [[2001#Zamolodchikov, Zamolodchikov]]: ZZ branes
- [[2000#Fateev, Zamolodchikov, Zamolodchikov]] and [[2000#Teschner]]: FZZT branes
- [[2001#Ponsot, Teschner]]: boundary 3-point function
- [[2001#Hosomichi]]: bulk-to-boundary OPEs
- [[2023#Ang, Remy, Sun, Zhu]]: reproduces boundary 3-point function and bulk-boundary propagator from probabilistic approach and relates them to [[0573 Crossing kernel|fusion and modular kernels]] respectively
## Related topics
- [[0562 Liouville theory]]
- [[0658 FZZT brane]]