The Open String Regge Trajectory and Its Field Theory Limit

We study the properties of the leading Regge trajectory in open string theory including the open string planar one-loop corrections. With SU(N) Chan-Paton factors, the sum over planar open string multi-loop diagrams describes the 't Hooft limit N\to\infty. Our motivation is to improve the understanding of open string theory at finite \alpha' as a model of gauge theories. SU(N) gauge theories in D space-time dimensions are described by requiring open strings to end on a stack of N Dp-branes of space-time dimension D=p+1. The large N leading trajectory \alpha(t)=1+\alpha' t+\Sigma(t) can be extracted, through order g^2, from the s\to-\infty limit, at fixed t, of the four open string tree and planar loop diagrams. We analyze the t\to0 behavior with the result that \Sigma(t)\sim-Cg^2(-\alpha' t)^{(D-4)/2}/(D-4). This result precisely tracks the 1-loop Reggeized gluon of gauge theory in D>4 space-time dimensions. In particular, for D\to4 it reproduces the known infrared divergences of gauge theory in 4 dimensions with a Regge trajectory behaving as -\ln(-\alpha^\prime t). We also study \Sigma(t) in the limit t\to-\infty and show that, when D<8, it behaves as \alpha^\prime t/(\ln(-\alpha^\prime t))^{\gamma}, where \gamma>0 depends on D and the number of massless scalars. Thus, as long as 4<D<8, the 1-loop correction stays small relative to the tree trajectory for the whole range -\infty<t<0. Finally we present the results of numerical calculations of \Sigma(t) for all negative t.Comment: 19 pages, 5 figure

Threshold quantile autoregressive models

We study in this article threshold quantile autoregressive processes. In particular we propose estimation and inference of the parameters in nonlinear quantile processes when the threshold parameter defining nonlinearities is known for each quantile, and also when the parameter vector is estimated consistently. We derive the asymptotic properties of the nonlinear threshold quantile autoregressive estimator. In addition, we develop hypothesis tests for detecting threshold nonlinearities in the quantile process when the threshold parameter vector is not identified under the null hypothesis. In this case we propose to approximate the asymptotic distribution of the composite test using a p-value transformation. This test contributes to the literature on nonlinearity tests by extending Hansen’s (Econometrica 64, 1996, pp.413-430) methodology for the conditional mean process to the entire quantile process. We apply the proposed methodology to model the dynamics of US unemployment growth after the Second World War. The results show evidence of important heterogeneity associated with unemployment, and strong asymmetric persistence on unemployment growth

Chemical potential as a source of stability for gravitating Skyrmions

A discussion of the stability of self gravitating Skyrmions, with a large winding number N, in a Schwarzschild type of metric, is presented for the case where an isospin chemical potential is introduced. It turns out that the chemical potential stabilizes the behavior of the Skyrmion discussed previously in the literature. This analysis is carried on in the framework of a variational approach using different ansaetze for the radial profile of the Skyrmion. We found a divergent behavior for the size of the Skyrmion, associated to a certain critical value $\mu_c$ of the chemical potential. At this point, the mass of the Skyrmion vanishes. $\mu_c$ is essentialy independent of gravitating effects. The stability of a large N skyrmion against decays into single particles is also discussed.Comment: 10 pages, 4 figures Small changes to the previous version and a new referenc