  Boundary conformal field theory (BCFT) is the study of conformal field theory
(CFT) on manifolds with a boundary. We can use conformal symmetry to constrain
correlation functions of conformal invariant fields. We compute two-point and
three-point functions of conformal invariant fields which live in semi-infinite
space. For a situation with a boundary condition in surface $z=\bar{z}$
($t=0$), the results agree with gravity dual results. We also explore
representations of conformal group in two dimensions.
