On the Consistency of Orbifolds

Modular invariance is a necessary condition for the consistency of any closed string theory. In particular, it imposes stringent constraints on the spectrum of orbifold theories, and in principle determines their spectrum uniquely up to discrete torsion classes. In practice, however, there are often ambiguities in the construction of orbifolds that are a consequence of the fact that the action of the orbifold elements on degenerate ground states is not unambiguous. We explain that there exists an additional consistency condition, related to the spectrum of D-branes in the theory, which eliminates these ambiguities. For supersymmetric orbifolds this condition turns out to be equivalent to the condition that supersymmetry is unbroken in the twisted sectors, but for non-supersymmetric orbifolds it appears to be a genuinely new consistency condition.Comment: 10 pages, LaTex. The sign ambiguities in the GSO-projection are clarified in the abstract and the introduction, and revised in sections 3 and 4. In particular we clarify that modular invariance fixes all the ambiguities in principle, but in practice this is hard to do. The final conclusion regarding the spectrum of the non-supersymmetric orbifold remains unchange

Stable non-BPS D-particles

It is shown that the orbifold of type IIB string theory by (-1)^{F_L} I_4 admits a stable non-BPS Dirichlet particle that is stuck on the orbifold fixed plane. It is charged under the SO(2) gauge group coming from the twisted sector, and transforms as a long multiplet of the D=6 supersymmetry algebra. This suggests that it is the strong coupling dual of the perturbative stable non-BPS state that appears in the orientifold of type IIB by \Omega I_4.Comment: 10 pages, LaTe

Dualities of Type 0 Strings

It is conjectured that the two closed bosonic string theories, Type 0A and Type 0B, correspond to certain supersymmetry breaking orbifold compactifications of M-theory. Various implications of this conjecture are discussed, in particular the behaviour of the tachyon at strong coupling and the existence of non-perturbative fermionic states in Type 0A. The latter are shown to correspond to bound states of Type 0A D-particles, thus providing further evidence for the conjecture. We also give a comprehensive description of the various Type 0 closed and open string theories.Comment: 23 pages LaTex, 1 figure. Error corrected in table 1. Version to appear in JHE

Non-BPS States in Heterotic - Type IIA Duality

The relation between some perturbative non-BPS states of the heterotic theory on T^4 and non-perturbative non-BPS states of the orbifold limit of type IIA on K3 is exhibited. The relevant states include a non-BPS D-string, and a non-BPS bound state of BPS D-particles (`D-molecule'). The domains of stability of these states in the two theories are determined and compared.Comment: 17 pages LaTex, 1 figure; Minor correction in subsection 4.

Effect of 2-Substitution on the Rearrangement of 1-Cyclopropylvinyl Cations

2-Substitution in 1-cyclopropylvinyl cations produces a steric effect on cation generation and solvent trapping, but an electronic charge-stabilizing effect on cyclopropyl-to-cyclobutyl rearrangement

3-Oxabicyclo[3,2,0]hepta-1,4-diene

3-Oxabicyclo[3,2,0]hepta-1,4-diene (3) has been synthesized by partial hydrogenation of 3-oxabicyclo-[3,2,0]hepta-1,4,6-triene (2)

Generalized Paraxial Ray Trace Procedure Derived from Geodesic Deviation

Paraxial ray tracing procedures have become widely accepted techniques for acoustic models in seismology and underwater acoustics. To date a generic form of these procedures including fluid motion and time dependence has not appeared in the literature. A detailed investigation of the characteristic curves of the equations of hydrodynamics allows for an immediate generalization of the procedure to be extracted from the equation form geodesic deviation. The general paraxial ray trace equations serve as an ideal supplement to ordinary ray tracing in predicting the deformation of acoustic beams in random environments. The general procedure is derived in terms of affine parameterization and in a coordinate time parameterization ideal for application to physical acoustic ray propagation. The formalism is applied to layered media, where the deviation equation reduces to a second order differential equation for a single field with a general solution in terms of a depth integral along the ray path. Some features are illustrated through special cases which lead to exact solutions in terms of either ordinary or special functions.Comment: Original; 40 pages (double spaced), 1 figure Replaced version; 36 pages single spaced, 7 figures. Expanded content; Complete derivation of the equations from the equations of hydrodynamics, introduction of an auxiliary basis for three dimensional wave-front modeling. Typos in text and equations correcte