Perturbative Gravity and Gauge Theory Relations -- A Review

This review is dedicated to the amazing Kawai-Lewellen-Tye relations, connecting perturbative gravity and gauge theories at tree level. The main focus is on n-point derivations and general properties both from a string theory and pure field theory point of view. In particular the field theory part is based on some very recent developments.Comment: 29 pages, 5 figures. Invited review for a special issue of Advances in High Energy Physics devoted to "Gauge/String Duality 2011

New Relations for Gauge-Theory Amplitudes with Matter

We extend a recently discovered set of relations for gauge-theory amplitudes to non-gluonic matter. For all MHV amplitudes we find that these can be made to hold for scalar/fermion/quark cases by inclusion of a factor derived via Ward identities. For six- and seven-point amplitudes with non-gluonic matter we explicitly confirm these relations for NMHV helicity configurations.Comment: 14 pages, added content, added reference

Using Instrumental Variables to Estimate the Share of Backward- Looking Firms

This paper examines the small-sample distribution of the instrumental variables (IV) estimation procedure employed by Gali and Gertler (1999) to assess the empirical fit of the New Keynesian Phillips Curve (NKPC) and the hybrid Phillips Curve (HPC). Their estimation method is now widely used to assess the importance of firms that act in a backward- looking manner. Unfortunately, the IV method is highly sensitive to the way the hybrid model is normalized. Using Monte Carlo simulations, I find that one normalization used by Gali and Gertler (and others) finds evidence of backward-looking firms even when there is none by construction. In addition, the IV estimates are also sensitive to the choice of normalization in a broader range of specifications. Using Monte Carlo experiments, I identify which normalizations work better than others. Finally, I find that the bootstrapped standard errors are, not surprisingly, bigger than the asymptotic ones reported by Gali and Gertler. When using my preferred normalization, I find that the NKPC is rejected at the 5 percent but not at the 1 percent level.New Keynesian Phillips Curve; Hybrid Phillips Curve; Normalization

Feynman Rules for QCD in Space-Cone Gauge

We present the Lagrangian and Feynman rules for QCD written in space-cone gauge and after eliminating unphysical degrees of freedom from the gluonic sector. The main goal is to clarify and allow for straightforward application of these Feynman rules. We comment on the connection between BCFW recursion relations and space-cone gauge.Comment: 7 pages, typos corrected, diagrams and clarifying text adde

Using Instrumental Varibles to Estimate the Share of Backward- Looking Firms

This paper examines the small-sample distribution of the instrumental variables (IV) estimation procedure employed by Gali and Gertler (1999) to assess the empirical fit of the New Keynesian Phillips Curve (NKPC) and the hybrid Phillips Curve (HPC). Their estimation method is now widely used to assess the importance of firms that act in a backward-looking manner. Unfortunately, the IV method is highly sensitive to the way the hybrid model is normalized. Using Monte Carlo simulations, I find that one normalization used by Gali and Gertler (and others) finds evidence of backward-looking firms even when there is none by construction. In addition, the IV estimates are also sensitive to the choice of normalization in a broader range of specifications. Using Monte Carlo experiments, I identify which normalizations work better than others. Finally, I find that the bootstrapped standard errors are, not surprisingly, bigger than the asymptotic ones reported by Gali and Gertler. When using my preferred normalization, I find that the NKPC is rejected at the 5 percent but not at the 1 percent levelNew Keynesian Phillips Curve; Hybrid Phillips Curve; Normalization

Resolving isospectral "drums" by counting nodal domains

Several types of systems were put forward during the past decades to show that there exist {\it isospectral} systems which are {\it metrically} different. One important class consists of Laplace Beltrami operators for pairs of flat tori in $\mathbb{R}^n$ with $n\geq 4$. We propose that the spectral ambiguity can be resolved by comparing the nodal sequences (the numbers of nodal domains of eigenfunctions, arranged by increasing eigenvalues). In the case of isospectral flat tori in four dimensions - where a 4-parameters family of isospectral pairs is known- we provide heuristic arguments supported by numerical simulations to support the conjecture that the isospectrality is resolved by the nodal count. Thus - one can {\it count} the shape of a drum (if it is designed as a flat torus in four dimensions...).Comment: 13 pages, 3 figure

Measurements of Solid Spheres Bouncing Off Flat Plates

Recent years have seen a substantial increase of interest in the flows of granular materials whose rheology is dominated by the physical contact between particles and between particles and the containing walls. Considerable advances in the theoretical understanding of rapid granular material flows have been made by the application of the statistical methods of molecular gas dynamics (e.g., Jenkins and Savage (1983), Lun et al. (1984)) and by the use of computers simulations of these flows (e.g., Campbell and Brennen (1985), Walton (1984)). Experimental studies aimed at measurements of the fundamental rheology properties are much less numerous and are understandably limited by the great difficulties involved in trying to measure velocity profiles, solid fraction profiles, and fluctuating velocities within a flowing granular material. Nevertheless, it has become clear that one of the most severe problems encountered when trying to compare experimental data with the theoretical models is the uncertainty in the material properties governing particle/particle or particle/wall collisions. Many of the theoretical models and computer simulations assume a constant coefficient of restitution (and, in some cases, a coefficient of friction). The purpose of the present project was to provide some documentation for particle/wall collisions by means of a set of relatively simple experiments in which solid spheres of various diameters and materials were bounced off plates of various thickness and material. The objective was to provide the kind of information on individual particle/wall collisions needed for the theoretical rheological models and computer simulations of granular material flows: in particular, to help resolve some of the issues associated with the boundary condition at a solid wall. For discussion of the complex issues associated with dynamic elastic or inelastic impact, reference is made to Goldsmith (1960) and the recent text by Johnson (1985)

Investment and trade patterns in a sticky-price, open-economy model

This paper develops a tractable two-country DSGE model with sticky prices à la Calvo (1983) and local-currency pricing. We analyze the capital investment decision in the presence of adjustment costs of two types, the capital adjustment cost (CAC) specification and the investment adjustment cost (IAC) specification. We compare the investment and trade patterns with adjustment costs against those of a model without adjustment costs and with (quasi-) flexible prices. We show that having adjustment costs results into more volatile consumption and net exports, and less volatile investment. We document three important facts on U.S. trade: a) the S-shaped cross-correlation function between real GDP and the real net exports share, b) the J-curve between terms of trade and net exports, and c) the weak and S-shaped cross-correlation between real GDP and terms of trade. We find that adding adjustment costs tends to reduce the model's ability to match these stylized facts. Nominal rigidities cannot account for these features either.Macroeconomics - Econometric models ; Capital investments ; International trade ; Foreign exchange

Asymptotics of high order noise corrections

We consider an evolution operator for a discrete Langevin equation with a strongly hyperbolic classical dynamics and noise with finite moments. Using a perturbative expansion of the evolution operator we calculate high order corrections to its trace in the case of a quartic map and Gaussian noise. The leading contributions come from the period one orbits of the map. The asymptotic behaviour is investigated and is found to be independent up to a multiplicative constant of the distribution of noise.Comment: 5 pages, 6 figures, submitted to J. Stat. Phy