Thermalization of Poincar\'{e} Vacuum State and Fermion Emission from AdS_3 Black Holes in Bulk-Boundary Correspondence

The greybody factors for spin 1/2 particles in the BTZ black holes are discussed from 2D CFT in bulk-boundary correspondence. It is found that the initial state of spin 1/2 particle in the BTZ black holes can be described by the Poincar'{e} vacuum state in boundary 2D CFT, and the nonlinear coordinate transformation causes the thermalization of the Poincar'{e} vacuum state. For special case, our results for the greybody factors agree with the semiclassical calculation.