Beta Functions of Orbifold Theories and the Hierarchy Problem

We examine a class of gauge theories obtained by projecting out certain fields from an N=4 supersymmetric SU(N) gauge theory. These theories are non-supersymmetric and in the large N limit are known to be conformal. Recently it was proposed that the hierarchy problem could be solved by embedding the standard model in a theory of this kind with finite N. In order to check this claim one must find the conformal points of the theory. To do this we calculate the one-loop beta functions for the Yukawa and quartic scalar couplings. We find that with the beta functions set to zero the one-loop quadratic divergences are not canceled at sub-leading order in N; thus the hierarchy between the weak scale and the Planck scale is not stabilized unless N is of the order 10^28 or larger. We also find that at sub-leading orders in N renormalization induces new interactions, which were not present in the original Lagrangian.Comment: 21 pages, LaTeX, 6 figures. Minor clarifications, references adde

Impact of massive neutrinos on the Higgs self-coupling and electroweak vacuum stability

The presence of right-handed neutrinos in the type I seesaw mechanism may lead to significant corrections to the RG evolution of the Higgs self-coupling. Compared to the Standard Model case, the Higgs mass window can become narrower, and the cutoff scale become lower. Naively, these effects decrease with decreasing right-handed neutrino mass. However, we point out that the unknown Dirac Yukawa matrix may impact the vacuum stability constraints even in the low scale seesaw case not far away from the electroweak scale, hence much below the canonical seesaw scale of 10^15 GeV. This includes situations in which production of right-handed neutrinos at colliders is possible. We illustrate this within a particular parametrization of the Dirac Yukawas and with explicit low scale seesaw models. We also note the effect of massive neutrinos on the top quark Yukawa coupling, whose high energy value can be increased with respect to the Standard Model case.Comment: 17 pages, 7 figures, minor revisions, version to appear in JHE

Collisional Dark Matter and the Origin of Massive Black Holes

If the cosmological dark matter is primarily in the form of an elementary particle which has cross section and mass for self-interaction having a ratio similar to that of ordinary nuclear matter, then seed black holes (formed in stellar collapse) will grow in a Hubble time, due to accretion of the dark matter, to a mass range 10^6 - 10^9 solar masses. Furthermore, the dependence of the final black hole mass on the galaxy velocity dispersion will be approximately as observed and the growth rate will show a time dependence consistent with observations. Other astrophysical consequences of collisional dark matter and tests of the idea are noted.Comment: 7 pages, no figures, LaTeX2e, Accepted for publication in Phys. Rev. Lett. Changed conten

Limit Cycles in Four Dimensions

We present an example of a limit cycle, i.e., a recurrent flow-line of the beta-function vector field, in a unitary four-dimensional gauge theory. We thus prove that beta functions of four-dimensional gauge theories do not produce gradient flows. The limit cycle is established in perturbation theory with a three-loop calculation which we describe in detail.Comment: 12 pages, 1 figure. Significant revision of the interpretation of our result. Improved description of three-loop calculatio

Feedback from the IR Background in the Early Universe

It is commonly believed that the earliest stages of star-formation in the Universe were self-regulated by global radiation backgrounds - either by the ultraviolet Lyman-Werner (LW) photons emitted by the first stars (directly photodissociating H_2), or by the X-rays produced by accretion onto the black hole (BH) remnants of these stars (heating the gas but catalyzing H_2 formation). Recent studies have suggested that a significant fraction of the first stars may have had low masses (a few M_sun). Such stars do not leave BH remnants and they have softer spectra, with copious infrared (IR) radiation at photon energies around 1eV. Similar to LW and X-ray photons, these photons have a mean-free path comparable to the Hubble distance, building up an early IR background. Here we show that if soft-spectrum stars, with masses of a few M_sun, contributed more than 1% of the UV background (or their mass fraction exceeded 90%), then their IR radiation dominated radiative feedback in the early Universe. The feedback is different from the UV feedback from high-mass stars, and occurs through the photo-detachment of H^- ions, necessary for efficient H_2 formation. Nevertheless, we find that the baryon fraction which must be incorporated into low-mass stars in order to suppress H_2-cooling is only a factor of few higher than for high-mass stars.Comment: Accepted for publication in MNRAS (Letters). 5 pages with 2 figure

Four Generations: SUSY and SUSY Breaking

We revisit four generations within the context of supersymmetry. We compute the perturbativity limits for the fourth generation Yukawa couplings and show that if the masses of the fourth generation lie within reasonable limits of their present experimental lower bounds, it is possible to have perturbativity only up to scales around 1000 TeV. Such low scales are ideally suited to incorporate gauge mediated supersymmetry breaking, where the mediation scale can be as low as 10-20 TeV. The minimal messenger model, however, is highly constrained. While lack of electroweak symmetry breaking rules out a large part of the parameter space, a small region exists, where the fourth generation stau is tachyonic. General gauge mediation with its broader set of boundary conditions is better suited to accommodate the fourth generation.Comment: 27 pages, 5 figure

High-Resolution Quantification of Focal Adhesion Spatiotemporal Dynamics in Living Cells

Focal adhesions (FAs) are macromolecular complexes that provide a linkage between the cell and its external environment. In a motile cell, focal adhesions change size and position to govern cell migration, through the dynamic processes of assembly and disassembly. To better understand the dynamic regulation of focal adhesions, we have developed an analysis system for the automated detection, tracking, and data extraction of these structures in living cells. This analysis system was used to quantify the dynamics of fluorescently tagged Paxillin and FAK in NIH 3T3 fibroblasts followed via Total Internal Reflection Fluorescence Microscopy (TIRF). High content time series included the size, shape, intensity, and position of every adhesion present in a living cell. These properties were followed over time, revealing adhesion lifetime and turnover rates, and segregation of properties into distinct zones. As a proof-of-concept, we show how a single point mutation in Paxillin at the Jun-kinase phosphorylation site Serine 178 changes FA size, distribution, and rate of assembly. This study provides a detailed, quantitative picture of FA spatiotemporal dynamics as well as a set of tools and methodologies for advancing our understanding of how focal adhesions are dynamically regulated in living cells. A full, open-source software implementation of this pipeline is provided at http://gomezlab.bme.unc.edu/tools

Observing the First Stars and Black Holes

The high sensitivity of JWST will open a new window on the end of the cosmological dark ages. Small stellar clusters, with a stellar mass of several 10^6 M_sun, and low-mass black holes (BHs), with a mass of several 10^5 M_sun should be directly detectable out to redshift z=10, and individual supernovae (SNe) and gamma ray burst (GRB) afterglows are bright enough to be visible beyond this redshift. Dense primordial gas, in the process of collapsing from large scales to form protogalaxies, may also be possible to image through diffuse recombination line emission, possibly even before stars or BHs are formed. In this article, I discuss the key physical processes that are expected to have determined the sizes of the first star-clusters and black holes, and the prospect of studying these objects by direct detections with JWST and with other instruments. The direct light emitted by the very first stellar clusters and intermediate-mass black holes at z>10 will likely fall below JWST's detection threshold. However, JWST could reveal a decline at the faint-end of the high-redshift luminosity function, and thereby shed light on radiative and other feedback effects that operate at these early epochs. JWST will also have the sensitivity to detect individual SNe from beyond z=10. In a dedicated survey lasting for several weeks, thousands of SNe could be detected at z>6, with a redshift distribution extending to the formation of the very first stars at z>15. Using these SNe as tracers may be the only method to map out the earliest stages of the cosmic star-formation history. Finally, we point out that studying the earliest objects at high redshift will also offer a new window on the primordial power spectrum, on 100 times smaller scales than probed by current large-scale structure data.Comment: Invited contribution to "Astrophysics in the Next Decade: JWST and Concurrent Facilities", Astrophysics & Space Science Library, Eds. H. Thronson, A. Tielens, M. Stiavelli, Springer: Dordrecht (2008

Photodissociation of H2 in Protogalaxies: Modeling Self-Shielding in 3D Simulations

The ability of primordial gas to cool in proto-galactic haloes exposed to Lyman-Werner (LW) radiation is critically dependent on the self-shielding of H_2. We perform radiative transfer calculations of LW line photons, post-processing outputs from three-dimensional adaptive mesh refinement (AMR) simulations of haloes with T_vir > 10^4 K at redshifts around z=10. We calculate the optically thick photodissociation rate numerically, including the effects of density, temperature, and velocity gradients in the gas, as well as line overlap and shielding of H_2 by HI, over a large number of sight-lines. In low-density regions (n<10^4 cm^-3) the dissociation rates exceed those obtained using most previous approximations by more than an order of magnitude; the correction is smaller at higher densities. We trace the origin of the deviations primarily to inaccuracies of (i) the most common fitting formula (Draine & Bertoldi 1996) for the suppression of the dissociation rate and (ii) estimates for the effective shielding column density from local properties of the gas. The combined effects of gas temperature and velocity gradients are comparatively less important, typically altering the spherically averaged rate only by a factor of less than two. We present a simple modification to the DB96 fitting formula for the optically thick rate which improves agreement with our numerical results to within approx. 15 per cent, and can be adopted in future simulations. We find that estimates for the effective shielding column can be improved by using the local Sobolev length. Our correction to the H_2 self-shielding reduces the critical LW flux to suppress H_2-cooling in T_vir>10^4 K haloes by an order of magnitude; this increases the number of such haloes in which supermassive (approx. M=10^5 M_sun) black holes may have formed.Comment: 17 pages, 11 figures. Submitted to MNRA