Greybody Factors in the $AdS_3$/CFT Correspondence

Abstract

We propose a new method to calculate the greybody factor in the $AdS_3$. This is based on both the non-normalizable modes of a test field($\Phi_i$) and $AdS_3$/CFT correspondence. Such non-normalizable modes serve as classical, non-fluctuating background and encode the choice of operator insertion(${\cal O}^i$) in the boundary. Actually specifying the boundary condition at infinity of $AdS_3$ corresponds to turning on these non-normalizable modes. Hence we can calculate the greybody factor of test fields without the Dirichlet(or Neumann) boundary condition. The result is consistent with those of the boundary CFT and effective string calculations.