Boundary Fluctuations of AdS String

We analyse the world-sheet perturbations of string theory formulated around $AdS_3$ background. We identify a set of operators that, while added to the world-sheet action, generate the boundary fluctuations of $AdS_3$. The effect of these operators can be collectively defined in terms of Liouville field living on the $AdS_3$ boundary. We then study various deformations of $AdS_3$ generated by boundary fluctuations by turning on suitable world-sheet couplings. We also discuss certain small fluctuations around the BTZ black hole.Comment: 10 pages, harvmac, no figur

Holonomies, anomalies and the Fefferman-Graham ambiguity in AdS3 gravity

Using the Chern-Simon formulation of (2+1) gravity, we derive, for the general asymptotic metrics given by the Fefferman-Graham-Lee theorems, the emergence of the Liouville mode associated to the boundary degrees of freedom of (2+1) dimensional anti de Sitter geometries. Holonomies are described through multi-valued gauge and Liouville fields and are found to algebraically couple the fields defined on the disconnected components of spatial infinity. In the case of flat boundary metrics, explicit expressions are obtained for the fields and holonomies. We also show the link between the variation under diffeomorphisms of the Einstein theory of gravitation and the Weyl anomaly of the conformal theory at infinity.Comment: LaTeX, 26 pages, 1 figure, modified version that will appear in Nucl. Phys.

Quantum effective action from the AdS/CFT correspondence

We obtain an Einstein metric of constant negative curvature given an arbitrary boundary metric in three dimensions, and a conformally flat one given an arbitrary conformally flat boundary metric in other dimensions. In order to compute the on-shell value of the gravitational action for these solutions, we propose to integrate the radial coordinate from the boundary till a critical value where the bulk volume element vanishes. The result, which is a functional of the boundary metric, provides a sector of the quantum effective action common to all conformal field theories that have a gravitational description. We verify that the so-defined boundary effective action is conformally invariant in odd (boundary) dimensions and has the correct conformal anomaly in even (boundary) dimensions. In three dimensions and for arbitrary static boundary metric the bulk metric takes a rather simple form. We explicitly carry out the computation of the corresponding effective action and find that it equals the non-local Polyakov action.Comment: 12 pages, latex, no figures; v2: minor improvements and two references adde

Uniqueness of the asymptotic AdS3 geometry

We explicitly show that in (2+1) dimensions the general solution of the Einstein equations with negative cosmological constant on a neigbourhood of timelike spatial infinity can be obtained from BTZ metrics by coordinate transformations corresponding geometrically to deformations of their spatial infinity surface. Thus, whatever the topology and geometry of the bulk, the metric on the timelike extremities is BTZ.Comment: LaTeX, 8 pages, no figures, version that will appear in Class. Quant. Gra

Conformal description of horizon's states

The existence of black hole horizon is considered as a boundary condition to be imposed on the fluctuating metrics. The coordinate invariant form of the condition for class of spherically symmetric metrics is formulated. The diffeomorphisms preserving this condition act in (arbitrary small) vicinity of the horizon and form the group of conformal transformations of two-dimensional space ($r-t$ sector of the total space-time). The corresponding algebra recovered at the horizon is one copy of the Virasoro algebra. For general relativity in $d$ dimensions we find an effective two-dimensional theory governing the conformal dynamics at the horizon universally for any $d\geq 3$. The corresponding Virasoro algebra has central charge $c$ proportional to the Bekenstein-Hawking entropy. Identifying the zero-mode configuration we calculate $L_0$. The counting of states of this horizon's conformal field theory by means of Cardy's formula is in complete agreement with the Bekenstein-Hawking expression for the entropy of black hole in $d$ dimensions.Comment: 13 pages, latex, no figures; the final version to appear in Phys. Lett.

Aspects of Diffeomorphism and Conformal invariance in classical Liouville theory

The interplay between the diffeomorphism and conformal symmetries (a feature common in quantum field theories) is shown to be exhibited for the case of black holes in two dimensional classical Liouville theory. We show that although the theory is conformally invariant in the near horizon limit, there is a breaking of the diffeomorphism symmetry at the classical level. On the other hand, in the region away from the horizon, the conformal symmetry of the theory gets broken with the diffeomorphism symmetry remaining intact.Comment: Accepted in Euro. Phys. Letters., Title changed, abstract modified, major modifications made in the pape

Statistical Entropy of BTZ Black Hole in Higher Curvature Gravity

For the BTZ black hole in the Einstein gravity, a statistical entropy has been calculated to be equal to the Bekenstein-Hawking entropy. In this paper, the statistical entropy of the BTZ black hole in the higher curvature gravity is calculated and shown to be equal to the one derived by using the Noether charge method. This suggests that the equivalence of the geometrical and statistical entropies of the black hole is retained in the general diffeomorphism invariant theories of gravity. A relation between the cosmic censorship conjecture and the unitarity of the conformal field theory on the boundary of AdS is also discussed.Comment: 9 pages, no figure, submitted to Physics Letters

A Note on Einstein Gravity on AdS3_3 and Boundary Conformal Field Theory

We find a simple relation between the first subleading terms in the asymptotic expansion of the metric field in AdS$_3$, obeying the Brown-Henneaux boundary conditions, and the stress tensor of the underlying Liouville theory on the boundary. We can also provide an more explicit relation between the bulk metric and the boundary conformal field theory when it is described in terms of a free field with a background charge.Comment: LateX file, 10 page

Near Horizon Geometry and Black Holes in Four Dimensions

A large class of extremal and near-extremal four dimensional black holes in M-theory feature near horizon geometries that contain three dimensional asymptotically anti-de Sitter spaces. Globally, these geometries are derived from AdS_3 by discrete identifications. The microstates of such black holes can be counted by exploiting the conformal symmetry induced on the anti-de Sitter boundary, and the result agrees with the Bekenstein-Hawking area law. This approach, pioneered by Strominger, clarifies the physical nature of the black hole microstates. It also suggests that recent analyses of the relationship between boundary conformal field theory and supergravity can be extended to orbifolds of AdS spaces.Comment: 9 pages, LaTeX, small clarifications, references added, version to appear in Nucl. Phys.