Correlation functions of BCFT

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.