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|Paper IPM / Physic / 11449||
We show that for the certain limit of frequency, the wave equation of the massless scalar field in the background of the spacelike warped AdS_3 black hole can be written as the Casimir of the SL(2,R) symmetry.
Two set of SL(2,R) generators are found which identify hidden SL(2,R) SL(2,R) symmetry of the solution. This symmetry is only locally defined and is spontaneously broken to U(1) U(1) by periodic identification of coordinate. By using the generator of this identification we can read the left and right temperatures (T_L,T_R) of the dual conformal field theory which are in complete agreement with the WAdS/CFT conjecture. It is shown that generators of the hidden symmetry are locally the Killing vectors of the AdS_3 geometry. Moreover, under the above condition of the scalar wave frequency, absorption cross section of the scalar field is consistent with the two-point function of the dual CFT.
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