AdS${}_3$/CFT Correspondence, Poincar\'{e} Vacuum State and Greybody Factors in BTZ Black Holes

The greybody factors in BTZ black holes are evaluated from 2D CFT in the spirit of AdS${}_3$/CFT correspondence. The initial state of black holes in the usual calculation of greybody factors by effective CFT is described as Poincar'{e} vacuum state in 2D CFT. The normalization factor which cannot be fixed in the effective CFT without appealing to string theory is shown to be determined by the normalized bulk-to-boundary Green function. The relation among the greybody factors in different dimensional black holes is exhibited. Two kinds of $(h,\bar{h})=(1,1)$ operators which couple with the boundary value of massless scalar field are discussed.