The Number of States of Two Dimensional Critical String Theory

We discuss string theory vacua which have the wrong number of spacetime dimensions, and give a crude argument that vacua with more than four large dimensions are improbable. We then turn to two dimensional vacua, which naively appear to violate Bekenstein's entropy principle. A classical analysis shows that the naive perturbative counting of states is unjustified. All excited states of the system have strong coupling singularities which prevent us from concluding that they really exist. A speculative interpretation of the classical solutions suggests only a finite number of states will be found in regions bounded by a finite area. We also argue that the vacuum degeneracy of two dimensional classical string theory is removed in quantum mechanics. The system appears to be in a Kosterlitz-Thouless phase. This leads to the conclusion that it is also improbable to have only two large spacetime dimensions in string theory. However, we note that, unlike our argument for high dimensions, our conclusions about the ground state have neglected two dimensional quantum gravitational effects, and are at best incomplete.Comment: 12 pages, harvma

CPT and Other Symmetries in String/M Theory

We initiate a search for non-perturbative consistency conditions in M theory. Some non-perturbative conditions are already known in Type I theories; we review these and search for others. We focus principally on possible anomalies in discrete symmetries. It is generally believed that discrete symmetries in string theories are gauge symmetries, so anomalies would provide evidence for inconsistencies. Using the orbifold cosmic string construction, we give some evidence that the symmetries we study are gauged. We then search for anomalies in discrete symmetries in a variety of models, both with and without supersymmetry. In symmetric orbifold models we extend previous searches, and show in a variety of examples that all anomalies may be canceled by a Green-Schwarz mechanism. We explore some asymmetric orbifold constructions and again find that all anomalies may be canceled this way. Then we turn to Type IIB orientifold models where it is known that even perturbative anomalies are non-universal. In the examples we study, by combining geometric discrete symmetries with continuous gauge symmetries, one may define non-anomalous discrete symmetries already in perturbation theory; in other cases, the anomalies are universal. Finally, we turn to the question of CPT conservation in string/M theory. It is well known that CPT is conserved in all string perturbation expansions; here in a number of examples for which a non-perturbative formulation is available we provide evidence that it is conserved exactly.Comment: 52 pages.1 paragraph added in introduction to clarify assumption

Is There A String Theory Landscape

We examine recent claims of a large set of flux compactification solutions of string theory. We conclude that the arguments for AdS solutions are plausible. The analysis of meta-stable dS solutions inevitably leads to situations where long distance effective field theory breaks down. We then examine whether these solutions are likely to lead to a description of the real world. We conclude that one must invoke a strong version of the anthropic principle. We explain why it is likely that this leads to a prediction of low energy supersymmetry breaking, but that many features of anthropically selected flux compactifications are likely to disagree with experiment.Comment: 39 pages, Latex, ``Terminology surrounding the anthropic principle revised to conform with accepted usage. More history of the anthropic principle included. Various references added.

Ten Dimensional Black Hole and the D0-brane Threshold Bound State

We discuss the ten dimensional black holes made of D0-branes in the regime where the effective coupling is large, and yet the 11D geometry is unimportant. We suggest that these black holes can be interpreted as excitations over the threshold bound state. Thus, the entropy formula for the former is used to predict a scaling region of the wave function of the latter. The horizon radius and the mass gap predicted in this picture agree with the formulas derived from the classical geometry.Comment: 11 pages, harvmac; v2: typos corrected, argument for the convergence of two integrals improved, v3: one ref. adde

Model validation for a noninvasive arterial stenosis detection problem

Copyright @ 2013 American Institute of Mathematical SciencesA current thrust in medical research is the development of a non-invasive method for detection, localization, and characterization of an arterial stenosis (a blockage or partial blockage in an artery). A method has been proposed to detect shear waves in the chest cavity which have been generated by disturbances in the blood flow resulting from a stenosis. In order to develop this methodology further, we use both one-dimensional pressure and shear wave experimental data from novel acoustic phantoms to validate corresponding viscoelastic mathematical models, which were developed in a concept paper [8] and refined herein. We estimate model parameters which give a good fit (in a sense to be precisely defined) to the experimental data, and use asymptotic error theory to provide confidence intervals for parameter estimates. Finally, since a robust error model is necessary for accurate parameter estimates and confidence analysis, we include a comparison of absolute and relative models for measurement error.The National Institute of Allergy and Infectious Diseases, the Air Force Office of Scientific Research, the Deopartment of Education and the Engineering and Physical Sciences Research Council (EPSRC)

On the Possibility of Large Axion Decay Constants

The decay constant of the QCD axion is required by observation to be small compared to the Planck scale. In theories of "natural inflation," and certain proposed anthropic solutions of the cosmological constant problem, it would be interesting to obtain a large decay constant for axion-like fields from microscopic physics. String theory is the only context in which one can sensibly address this question. Here we survey a number of periodic fields in string theory in a variety of string vacua. In some examples, the decay constant can be parameterically larger than the Planck scale but the effective action then contains appreciable harmonics of order $f_A/M_p$. As a result, these fields are no better inflaton candidates than Planck scale axions.Comment: 17 pages, no figures, minor change mad