Black Hole Entropy in Two Dimensions

Black hole entropy is studied for an exactly solvable model of two-dimensional gravity\cite{rst1}, using recently developed Noether charge techniques\cite{wald1}. This latter approach is extended to accomodate the non-local form of the semiclassical effective action. In the two-dimensional model, the final black hole entropy can be expressed as a local quantity evaluated on the horizon. This entropy is shown to satisfy an increase theorem on either the global or apparent horizon of a two-dimensional black hole.Comment: 18 pages, latex McGill/94-22 (minor revisions; final version which will appear in Phys. Rev. D

Instability of Ultra-Spinning Black Holes

It has long been known that, in higher-dimensional general relativity, there are black hole solutions with an arbitrarily large angular momentum for a fixed mass. We examine the geometry of the event horizon of such ultra-spinning black holes and argue that these solutions become unstable at large enough rotation. Hence we find that higher-dimensional general relativity imposes an effective `Kerr-bound' on spinning black holes through a dynamical decay mechanism. Our results also give indications of the existence of new stationary black holes with `rippled' horizons of spherical topology. We consider various scenarios for the possible decay of ultra-spinning black holes, and finally discuss the implications of our results for black holes in braneworld scenarios.Comment: 21 pages, typo's corrected, ref's adde

Flow of low energy couplings in the Wilson renormalization group

A new form of the Wilson renormalization group equation is derived, in which the flow equations are, up to linear terms, proportional to a gradient flow. A set of co\"ordinates is found in which the flow of marginal, low-energy, couplings takes a gradient form, if relevant couplings are tuned to vanish.Comment: 9 pages, RevTeX. Version to appear in Phys. Rev.

Flows for rectangular matrix models

Several new results on the multicritical behavior of rectangular matrix models are presented. We calculate the free energy in the saddle point approximation, and show that at the triple-scaling point, the result is the same as that derived from the recursion formulae. In the triple-scaling limit, we obtain the string equation and a flow equation for arbitrary multicritical points. Parametric solutions are also examined for the limit of almost-square matrix models. This limit is shown to provide an explicit matrix model realization of the scaling equations proposed to describe open-closed string theory.Comment: 13 pages, LaTeX, McGill/93-2

Experimental Challenges for Quantum Gravity

The existence of a new fundamental scale may lead to modified dispersion relations for particles at high energies. Such modifications seem to be realized with the Planck scale in certain descriptions of quantum gravity. We apply effective field theory to this problem and identify dimension 5 operators that would lead to cubic modifications of dispersion relations for Standard Model particles. We also discuss other issues related to this approach including various experimental bounds on the strength of these interactions. Further we sketch a scenario where mixing of these operators with dimensions 3 and 4 due to quantum effects is minimal.Comment: QTS3 proceedings; review of hep-ph/0301124 plus extended discussio

The O(dd) Story of Massive Supergravity

The low energy effective action describing the standard Kaluza-Klein reduction of heterotic string theory on a d-torus possesses a manifest O(d,d+16) symmetry. We consider generalized Scherk-Schwarz reductions of the heterotic string to construct massive gauged supergravities. We show that the resulting action can still be written in a manifestly O(d,d+16) invariant form, however, the U-duality transformations also act on the mass parameters. The latter play the dual role of defining the scalar potential and the nonabelian structure constants. We conjecture that just as for the standard reduction, a subgroup of this symmetry corresponds to an exact duality symmetry of the heterotic string theory.Comment: 55 pages, latex, no figures, added a few references, published in JHEP05(1999)01