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

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

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.

Quantum information erasure inside black holes

An effective field theory for infalling observers in the vicinity of a quasi-static black hole is given in terms of a freely falling lattice discretization. The lattice model successfully reproduces the thermal spectrum of outgoing Hawking radiation, as was shown by Corley and Jacobson, but can also be used to model observations made by a typical low-energy observer who enters the black hole in free fall at a prescribed time. The explicit short distance cutoff ensures that, from the viewpoint of the infalling observer, any quantum information that entered the black hole more than a scrambling time earlier has been erased by the black hole singularity. This property, combined with the requirement that outside observers need at least of order the scrambling time to extract quantum information from the black hole, ensures that a typical infalling observer does not encounter drama upon crossing the black hole horizon in a theory where black hole information is preserved for asymptotic observers.Comment: 20 pages, 3 figures, some minor correction