On the Hyperbolic Structure of Moduli Spaces With 16 SUSYs

We study the asymptotic limits of the heterotic string theories compactified on tori. We find a bilinear form uniquely determined by dualities which becomes Lorentzian in the case of one spacetime dimension. For the case of the SO(32) theory, the limiting descriptions include SO(32) heterotic strings, type I, type IA and other T-duals, M-theory on K3, type IIA theory on K3 and type IIB theory on K3 and possibly new limits not understood yet.Comment: JHEP LaTeX, 19 pages, 1 eps-figure, report number adde

A nonsupersymmetric matrix orbifold

We construct the matrix description for a twisted version of the IIA string theory on S^1 with fermions antiperiodic around a spatial circle. The result is a 2+1-dimensional U(N) x U(N) nonsupersymmetric Yang-Mills theory with fermionic matter transforming in the (N,Nbar). The two U(N)'s are exchanged if one goes around a twisted circle of the worldvolume. Relations with Type 0 theories are explored and we find Type 0 matrix string limits of our gauge theory. We argue however that most of these results are falsified by the absence of SUSY nonrenormalization theorems and that the models do not in fact have a sensible Lorentz invariant space time interpretation.Comment: JHEP LaTeX, 22 page

Asymptotic Quasinormal Frequencies of Different Spin Fields in Spherically Symmetric Black Holes

We consider the asymptotic quasinormal frequencies of various spin fields in Schwarzschild and Reissner-Nordstr\"om black holes. In the Schwarzschild case, the real part of the asymptotic frequency is ln3 for the spin 0 and the spin 2 fields, while for the spin 1/2, the spin 1, and the spin 3/2 fields it is zero. For the non-extreme charged black holes, the spin 3/2 Rarita-Schwinger field has the same asymptotic frequency as that of the integral spin fields. However, the asymptotic frequency of the Dirac field is different, and its real part is zero. For the extremal case, which is relevant to the supersymmetric consideration, all the spin fields have the same asymptotic frequency, the real part of which is zero. For the imaginary parts of the asymptotic frequencies, it is interesting to see that it has a universal spacing of $1/4M$ for all the spin fields in the single-horizon cases of the Schwarzschild and the extreme Reissner-Nordstr\"om black holes. The implications of these results to the universality of the asymptotic quasinormal frequencies are discussed.Comment: Revtex, 17 pages, 3 eps figures; one table, some remarks and references added to section I

Dualities versus Singularities

We show that a subgroup of the modular group of M-theory compactified on a ten torus, implies the Lorentzian structure of the moduli space, that is usually associated with naive discussions of quantum cosmology based on the low energy Einstein action. This structure implies a natural division of the asymptotic domains of the moduli space into regions which can/cannot be mapped to Type II string theory or 11D Supergravity (SUGRA) with large radii. We call these the safe and unsafe domains. The safe domain is the interior of the future light cone in the moduli space while the unsafe domain contains the spacelike region and the past light cone. Within the safe domain, apparent cosmological singularities can be resolved by duality transformations and we briefly provide a physical picture of how this occurs. The unsafe domains represent true singularities where all field theoretic description of the physics breaks down. They violate the holographic principle. We argue that this structure provides a natural arrow of time for cosmology. All of the Kasner solutions, of the compactified SUGRA theory interpolate between the past and future light cones of the moduli space. We describe tentative generalizations of this analysis to moduli spaces with less SUSY.Comment: JHEP LaTeX, 23 pages, 1 eps-figure. Five references, a paragraph at the beginning of section 3 and an appendix adde