Thermalization of Poincaré Vacuum State and Fermion Emission from AdS3 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 Poincaré vacuum state in boundary 2D CFT, and the nonlinear coordinate transformation causes the thermalization of the Poincaré vacuum state. For special case, our results for the greybody factors agree with the semiclassical calculation. e-mail address: [email protected] e-mail address: [email protected], JSPS postdoctral fellow In recent years there has been great progress in our understanding of black hole physics from string and conformal field theories (CFT). For reviews on this subject, see refs. [1]. Through these studies, it has been gradually realized that some 5D and 4D black holes contain BTZ black holes [2] in the near-horizon region [3, 4], and higher-dimensional black hole physics is essentially encoded in that of BTZ black holes. In fact it has been shown in ref. [5] that the Bekenstein-Hawking entropy for 5D and 4D black holes can be related to the entropy of BTZ black holes by making use of U-duality. Though much work on the absorption and Hawking radiation in 5D and 4D black holes has also been made in the semiclassical analysis, D-brane picture, effective string model and effective 2D CFT in refs. [6]-[10], only recently one began to recognize that not only the Bekenstein-Hawking entropy but also the greybody factors in 5D and 4D black holes can be understood as effectively coming from the near-horizon BTZ geometry [11, 12, 13]. Since the recently discovered AdS/CFT correspondence [3, 14, 15] might play an important role in the fundamental quantum theory for the black holes via the nearhorizon BTZ black holes, it is natural to expect that the greybody factors in the black holes should be elucidated in the context of the AdS/CFT correspondence. Indeed the greybody factors for scalar fields have been derived by using the nearhorizon BTZ (AdS3) geometry and AdS/CFT correspondence [11, 12]. Especially in ref. [12], the initial state of scalar particles in BTZ black holes has been described by a Poincaré vacuum state in the boundary 2D CFT. The nonlinear coordinate transformation between the Poincaré coordinates (w+, w−) and the BTZ coordinates (u+, u−) induces a mapping of the operator O(w+, w−) to O(u+, u−) by Bogoliubov transformation, and the operator O(u+, u−) sees the Poincaré vacuum state as an excited mixed state, that is, they see the Poincaré vacuum state as thermal bath of excitations in BTZ modes [12, 16, 17]. The usual procedure to thermally average the initial state of scalar particles in the calculation of greybody factors is just to measure the Poincaré vacuum state by the operator O(u+, u−) in the BTZ coordinates, which means that the nonlinear coordinate transformation causes the thermalization of the Poincaré vacuum state. In this paper, we discuss the greybody factors for spin 1 2 particle in the BTZ black holes from AdS/CFT correspondence. Though there have been many studies of correlation functions in the boundary theory from the bulk-boundary correspondence [18, 19, 20],