M-Theory on the Orbifold C^2/Z_N

We construct M-theory on the orbifold C^2/Z_N by coupling 11-dimensional supergravity to a seven-dimensional Yang-Mills theory located on the orbifold fixed plane. It is shown that the resulting action is supersymmetric to leading non-trivial order in the 11-dimensional Newton constant. This action provides the starting point for a reduction of M-theory on G_2 spaces with co-dimension four singularities.Comment: 33 pages, Late

Monad Bundles in Heterotic String Compactifications

In this paper, we study positive monad vector bundles on complete intersection Calabi-Yau manifolds in the context of E8 x E8 heterotic string compactifications. We show that the class of such bundles, subject to the heterotic anomaly condition, is finite and consists of about 7000 models. We explain how to compute the complete particle spectrum for these models. In particular, we prove the absence of vector-like family anti-family pairs in all cases. We also verify a set of highly non-trivial necessary conditions for the stability of the bundles. A full stability proof will appear in a companion paper. A scan over all models shows that even a few rudimentary physical constraints reduces the number of viable models drastically.Comment: 35 pages, 4 figure

Infinite Divisibility in Euclidean Quantum Mechanics

In simple -- but selected -- quantum systems, the probability distribution determined by the ground state wave function is infinitely divisible. Like all simple quantum systems, the Euclidean temporal extension leads to a system that involves a stochastic variable and which can be characterized by a probability distribution on continuous paths. The restriction of the latter distribution to sharp time expectations recovers the infinitely divisible behavior of the ground state probability distribution, and the question is raised whether or not the temporally extended probability distribution retains the property of being infinitely divisible. A similar question extended to a quantum field theory relates to whether or not such systems would have nontrivial scattering behavior.Comment: 17 pages, no figure

Random Bit Multilevel Algorithms for Stochastic Differential Equations

We study the approximation of expectations \E(f(X)) for solutions $X$ of SDEs and functionals $f \colon C([0,1],\R^r) \to \R$ by means of restricted Monte Carlo algorithms that may only use random bits instead of random numbers. We consider the worst case setting for functionals $f$ from the Lipschitz class w.r.t.\ the supremum norm. We construct a random bit multilevel Euler algorithm and establish upper bounds for its error and cost. Furthermore, we derive matching lower bounds, up to a logarithmic factor, that are valid for all random bit Monte Carlo algorithms, and we show that, for the given quadrature problem, random bit Monte Carlo algorithms are at least almost as powerful as general randomized algorithms

Export production under exchange rate uncertainty

Given that a multinational enterprise can react flexibly upon exchange rate movements, international trade flows may be interpreted as an option. An enterprise will opt to export if the profits obtained from exporting under given exchange rate developments are greater than if foreign subsidiary sales were opted. Naturally, given negative exchange rate scenario situations, an enterprise will choose not to export. By virtue of a favorable exchange rate situation it may be more advantageous to implement the flexibility given by the inherent option exercise privilege. Interestingly, even taking account of entrepreneurial risk aversion aspects of enterprises, it is demonstrated that situations characterized by enhanced exchange rate volatility may still lead to greater export trade volumes. --Export,Exchange Rate Volatility,Risk Aversion,Real Option

Random Bit Quadrature and Approximation of Distributions on Hilbert Spaces

We study the approximation of expectations \E(f(X)) for Gaussian random elements $X$ with values in a separable Hilbert space $H$ and Lipschitz continuous functionals $f \colon H \to \R$. We consider restricted Monte Carlo algorithms, which may only use random bits instead of random numbers. We determine the asymptotics (in some cases sharp up to multiplicative constants, in the other cases sharp up to logarithmic factors) of the corresponding $n$-th minimal error in terms of the decay of the eigenvalues of the covariance operator of $X$. It turns out that, within the margins from above, restricted Monte Carlo algorithms are not inferior to arbitrary Monte Carlo algorithms, and suitable random bit multilevel algorithms are optimal. The analysis of this problem leads to a variant of the quantization problem, namely, the optimal approximation of probability measures on $H$ by uniform distributions supported by a given, finite number of points. We determine the asymptotics (up to multiplicative constants) of the error of the best approximation for the one-dimensional standard normal distribution, for Gaussian measures as above, and for scalar autonomous SDEs

Moving Five-Branes in Low-Energy Heterotic M-Theory

We construct cosmological solutions of four-dimensional effective heterotic M-theory with a moving five-brane and evolving dilaton and T modulus. It is shown that the five-brane generates a transition between two asymptotic rolling-radii solutions. Moreover, the five-brane motion always drives the solutions towards strong coupling asymptotically. We present an explicit example of a negative-time branch solution which ends in a brane collision accompanied by a small-instanton transition. The five-dimensional origin of some of our solutions is also discussed.Comment: 16 pages, Latex, 3 eps figure

Exploring Positive Monad Bundles And A New Heterotic Standard Model

A complete analysis of all heterotic Calabi-Yau compactifications based on positive two-term monad bundles over favourable complete intersection Calabi-Yau threefolds is performed. We show that the original data set of about 7000 models contains 91 standard-like models which we describe in detail. A closer analysis of Wilson-line breaking for these models reveals that none of them gives rise to precisely the matter field content of the standard model. We conclude that the entire set of positive two-term monads on complete intersection Calabi-Yau manifolds is ruled out on phenomenological grounds. We also take a first step in analyzing the larger class of non-positive monads. In particular, we construct a supersymmetric heterotic standard model within this class. This model has the standard model gauge group and an additional U(1)_{B-L} symmetry, precisely three families of quarks and leptons, one pair of Higgs doublets and no anti-families or exotics of any kind.Comment: 48 page

A Comprehensive Scan for Heterotic SU(5) GUT models

Compactifications of heterotic theories on smooth Calabi-Yau manifolds remains one of the most promising approaches to string phenomenology. In two previous papers, http://arXiv.org/abs/arXiv:1106.4804 and http://arXiv.org/abs/arXiv:1202.1757, large classes of such vacua were constructed, using sums of line bundles over complete intersection Calabi-Yau manifolds in products of projective spaces that admit smooth quotients by finite groups. A total of 10^12 different vector bundles were investigated which led to 202 SU(5) Grand Unified Theory (GUT) models. With the addition of Wilson lines, these in turn led, by a conservative counting, to 2122 heterotic standard models. In the present paper, we extend the scope of this programme and perform an exhaustive scan over the same class of models. A total of 10^40 vector bundles are analysed leading to 35,000 SU(5) GUT models. All of these compactifications have the right field content to induce low-energy models with the matter spectrum of the supersymmetric standard model, with no exotics of any kind. The detailed analysis of the resulting vast number of heterotic standard models is a substantial and ongoing task in computational algebraic geometry.Comment: 33 pages, Late