Mellin transforming the minimal model CFTs: AdS/CFT at strong curvature

Mack has conjectured that all conformal field theories are equivalent to string theories. We explore the example of the two-dimensional minimal model CFTs and confirm that the Mellin transformed amplitudes have the desired properties of string theory in three-dimensional anti-de Sitter spacetime.Comment: 7 page

Statistical entropy of two-dimensional dilaton de Sitter space

It has been proposed that a quantum group structure underlies de Sitter/Conformal field theory duality. These ideas are used to give a microscopic operator counting interpretation for the entropy of two-dimensional dilaton de Sitter space. This agrees with the Bekenstein-Hawking entropy up to a factor of order unity.Comment: 12 pages, 1 figure, revtex

Comments on a Covariant Entropy Conjecture

Recently Bousso conjectured the entropy crossing a certain light-like hypersurface is bounded by the surface area. We point out a number of difficulties with this conjecture.Comment: 7 pages, 2 figures, harvmac, eps

Renormalization Group Flows from Gravity in Anti-de Sitter Space versus Black Hole No-Hair Theorems

Black hole no-hair theorems are proven using inequalities that govern the radial dependence of spherically symmetric configurations of matter fields. In this paper, we analyze the analogous inequalities for geometries dual to renormalization group flows via the AdS/CFT correspondence. These inequalities give much useful information about the qualitative properties of such flows. For Poincare invariant flows, we show that generic flows of relevant or irrelevant operators lead to singular geometries. For the case of irrelevant operators, this leads to an apparent conflict with Polchinski's decoupling theorem, and we offer two possible resolutions to this problem.Comment: 13 pages, 3 figures, harvmac, epsf, references and comments adde

Conformal Models of Two-Dimensional Turbulence

Polyakov recently showed how to use conformal field theory to describe two-dimensional turbulence. Here we construct an infinite hierarchy of solutions, both for the constant enstrophy flux cascade, and the constant energy flux cascade. We conclude with some speculations concerning the stability and physical meaning of these solutions.Comment: 17 pages, PUPT-1362, uses harvmac and tables.tex (minor typos corrected

Eleven-Dimensional Lorentz Symmetry from SUSY Quantum Mechanics

The supermembrane in light-cone gauge gives rise to a supersymmetric quantum mechanics system with SU(N) gauge symmetry when the group of area preserving diffeomorphisms is suitably regulated. de Wit, Marquard and Nicolai showed how eleven-dimensional Lorentz generators can be constructed from these degrees of freedom at the classical level. In this paper, these considerations are extended to the quantum level and it is shown the algebra closes to leading nontrivial order at large N. A proposal is made for extending these results to Matrix theory by realizing longitudinal boosts as large N renormalization group transformations.Comment: 16 pages, harvma

Constraints on Higher Derivative Operators in the Matrix Theory Effective Lagrangian

The consistency of Matrix theory with supergravity requires that in the large N_c limit terms of order v^4 in the SU(N_c) Matrix effective potential are not renormalized beyond one loop in perturbation theory. For SU(2) gauge group, the required non-renormalization theorem was proven recently by Paban, Sethi and Stern. In this paper we consider the constraints supersymmetry imposes on these terms for groups SU(N_c) with N_c>2. Non-renormalization theorems are proven for certain tensor structures, including the structures that appear in the one-loop effective action. However it is expected other tensor structures can in general be present, which may suffer renormalization at three loops and beyond.Comment: 10 pages, harvmac, (Some equations corrected. Conclusions unchanged.

Black hole holography and mean field evolution

Holographic theories representing black holes are expected to exhibit quantum chaos. We argue if the laws of quantum mechanics are expected to hold for observers inside such black holes, then such holographic theories must have a mean field approximation valid for typical black hole states, and for timescales approaching the scrambling time. Using simple spin models as examples, we examine the predictions of such an approach for observers inside black holes, and more speculatively inside cosmological horizons.Comment: 11 pages, 5 figure