Rank-nlogarithmic conformal field theory in the BTZ black hole

Abstract

We construct the rank-n finite temperature logarithmic conformal field theory (LCFT) starting from the n-coupled scalar field theory in the BTZ black hole background. Its zero temperature limit reduces to a rank-n LCFT in the AdS3 background whose gravity dual is a polycritical gravity. We compute all two-point functions of a rank-n finite temperature LCFT. Using the retarded Green's functions on the boundary, we obtain quasinormal modes of scalar An which satisfies the 2n-th order linearized equation. Furthermore, the absorption cross section of An indicates a feature of ln n−1 [ωℓ]-correction to the Klein-Gordon mode.PACS numbers: 04.60. Kz, 04.50.Kd, Critical gravity based on higher-curvature terms in the AdS d+1 -spacetimes [1-4] has regarded as a toy model for quantum gravity. At the critical point of avoiding the ghosts, a degeneracy takes place and massive gravitons coincide with massless gravitons. All massive gravitons are replaced by an equal amount of logarithmic modes at the critical point, leading to the critical gravity (loggravity). According to the dictionary of AdS-LCFT correspondence, one finds that a rank-2 logarithmic conformal field theory (LCFT) is dual to a critical gravity [5][6][7].However, one has to face with the non-unitarity issue of the log-gravity theory because it contains higherderivative terms. In order to resolve this issue, a polycritical gravity with 2n(n > 2)-derivative was introduced to provide multiple critical points [8] whose CFT dual seems to be a rank-n LCFT. A consistent unitary truncation of polycritical gravity was performed at the linearized level for odd n, but not for even n [9].On the other hand, a n-coupled scalar field model in the AdS d+1 -spacetimes has been proposed as a toy model for a gravitational dual to a rank-n LCFT [10]. Introducing n − 1 auxiliary scalar fields, this model could be rewritten as a two-derivative theory. The critical point is obtained when all masse of the n-scalar fields degenerate. The n − 1 higher-order logarithmic modes appear as logarithmic partners of the Klein-Gordon scalar A 1 . This model is compared to the 2n-derivative Lee-Wick model where the odd n and the even n cases feature qualitative difference [11].In this Report, we will investigate a n-coupled scalar field model on the BTZ black hole background [12]. Our purpose is twofold. One is to recognize the difference in the AdS-LCFT correspondence between a n-coupled scalar field model on the AdS 3 -a rank-n (zero temperature) LCFT and a n-coupled scalar field model on the BTZ black hole-a rank-n finite temperature LCFT. The other is to compute the quasinormal frequencies of a field A n satisfying (∇ 2 B −m 2 ) n A n = 0 and the absorption cross * Electronic address: tymoon@sogang.ac.kr † Electronic address: ysmyung@inje.ac.kr section from scattering A n off the BTZ black hole by using the retarded Green's function of rank-n finite temperature LCFT. Actually, this computation is a formidable task when using a single scalar equationInstead, employing the n-coupled scalar ...

Geometrical Method for Thermal Instability of Nonlinearly Charged BTZ Black Holes

“…One of the interesting subjects for recent gravitational studies is the investigation of three-dimensional black holes [1][2][3][4][5][6][7][8][9]. Considering three-dimensional solutions helps us to find a profound insight in the black hole physics, quantum view of gravity, and also its relations to string theory [10][11][12][13][14].…”