Spacetime and the Holographic Renormalization Group

Anti-de Sitter (AdS) space can be foliated by a family of nested surfaces homeomorphic to the boundary of the space. We propose a holographic correspondence between theories living on each surface in the foliation and quantum gravity in the enclosed volume. The flow of observables between our ``interior'' theories is described by a renormalization group equation. The dependence of these flows on the foliation of space encodes bulk geometry.Comment: 12 page

Feynman Path Integral on the Noncommutative Plane

We formulate Feynman path integral on a non commutative plane using coherent states. The propagator for a free particle exhibits UV cut-off induced by the parameter of non commutativity.Comment: 7pages, latex 2e, no figures. Accepted for publication on J.Phys.

Hard Scattering and Gauge/String Duality

We consider high-energy fixed-angle scattering of glueballs in confining gauge theories that have supergravity duals. Although the effective description is in terms of the scattering of strings, we find that the amplitudes are hard (power law). This is a consequence of the warped geometry of the dual theory, which has the effect that in an inertial frame the string process is never in the soft regime. At small angle we find hard and Regge behaviors in different kinematic regions.Comment: 4 page

Mass Quantization of the Schwarzschild Black Hole

We examine the Wheeler-DeWitt equaton for a static, eternal Schwarzschild black hole in Kucha\v r-Brown variables and obtain its energy eigenstates. Consistent solutions vanish in the exterior of the Kruskal manifold and are non-vanishing only in the interior. The system is reminiscent of a particle in a box. States of definite parity avoid the singular geometry by vanishing at the origin. These definite parity states admit a discrete energy spectrum, depending on one quantum number which determines the Arnowitt-Deser-Misner (ADM) mass of the black hole according to a relation conjectured long ago by Bekenstein, $M \sim \sqrt{n}M_p$. If attention is restricted only to these quantized energy states, a black hole is described not only by its mass but also by its parity. States of indefinite parity do not admit a quantized mass spectrum.Comment: Change in eq. (13). Factors of 4 cleaned up. Refs. adde

Reduction without reduction: Adding KK-monopoles to five dimensional stationary axisymmetric solutions

We present a general method to add KK-monopole charge to any asymptotically flat stationary axisymmetric solution of five dimensional General Relativity. The technique exploits the underlying SL(3,R) invariance of the system by identifying a particular element of the symmetry group which changes the asymptotic boundary condition and adds KK-monopole charge. Furthermore, we develop a set of technical tools which allow us to apply the SL(3,R) transformations to solutions produced by the Inverse Scattering method. As an example of our methods, we construct the exact solution describing a static black ring carrying KK-monopole charge.Comment: 36 pages, 3 figures, LaTeX, minor typos fixe

Entropy and Action of Dilaton Black Holes

We present a detailed calculation of the entropy and action of $U(1)~2$ dilaton black holes, and show that both quantities coincide with one quarter of the area of the event horizon. Our methods of calculation make it possible to find an explanation of the rule $S = A/4$ for all static, spherically symmetric black holes studied so far. We show that the only contribution to the entropy comes from the extrinsic curvature term at the horizon, which gives $S = A/4$ independently of the charge(s) of the black hole, presence of scalar fields, etc. Previously, this result did not have a general explanation, but was established on a case-by-case basis. The on-shell Lagrangian for maximally supersymmetric extreme dilaton black holes is also calculated and shown to vanish, in agreement with the result obtained by taking the limit of the expression obtained for black holes with regular horizon.The physical meaning of the entropy is discussed in relation to the issue of splitting of extreme black holes.Comment: 15 p., SU-ITP-92-2

Tachyon Field Quantization and Hawking Radiation

We quantize the tachyon field in a static two dimensional dilaton gravity black hole background,and we calculate the Hawking radiation rate. We find that the thermal radiation flux, due to the tachyon field, is larger than the conformal matter one. We also find that massive scalar fields which do not couple to the dilaton, do not give any contribution to the thermal radiation, up to terms quadratic in the scalar curvature.Comment: 13 pages, Latex file, 1 figure available upon reques

Brane Baldness vs. Superselection Sectors

The search for intersecting brane solutions in supergravity is a large and profitable industry. Recently, attention has focused on finding localized forms of known `delocalized' solutions. However, in some cases, a localized version of the delocalized solution simply does not exist. Instead, localized separated branes necessarily delocalize as the separation is removed. This phenomenon is related to black hole no-hair theorems, i.e. `baldness.' We continue the discussion of this effect and describe how it can be understood, in the case of Dirichlet branes, in terms of the corresponding intersection field theory. When it occurs, it is associated with the quantum mixing of phases and lack of superselection sectors in low dimensional field theories. We find surprisingly wide agreement between the field theory and supergravity both with respect to which examples delocalize and with respect to the rate at which this occurs.Comment: 26 pages, ReVTeX, 2 figures, reference added, version to appear in PR

Four Dimensional Conformal Supergravity From AdS Space

Exploring the role of conformal theories of gravity in string theory, we show that the minimal (N=2) gauged supergravities in five dimensions induce the multiplets and transformations of N=1 four dimensional conformal supergravity on the spacetime boundary. N=1 Poincare supergravity can be induced by explicitly breaking the conformal invariance via a radial cutoff in the 5d space. The AdS/CFT correspondence relates the maximal gauged supergravity in five dimensions to N=4 super Yang-Mills on the 4d spacetime boundary. In this context we show that the conformal anomaly of the gauge theory induces conformal gravity on the boundary of the space and that this theory, via the renormalization group, encapsulates the gravitational dynamics of the skin of asymptotically AdS spacetimes. Our results have several applications to the AdS/CFT correspondence and the Randall-Sundrum scenario.Comment: 20 pages, LaTeX. v3. references and minor comments adde