Non-Abelian Monopoles, Vortices and Confinement

Three closely related issues will be discussed. Magnetic quarks having non-Abelian charges have been found recently to appear as the dominant infrared degrees of freedom in some vacua of softly broken N=2 supersymmetric QCD with SU(n_c) gauge group. Their condensation upon N=1 perturbation causes confinement and dynamical symmetry breaking. We argue that these magnetic quarks can be naturally related to the semiclassical non-Abelian monopoles of the type first discussed by Goddard, Nuyts, Olive and E. Weinberg. We discuss also general properties of non-Abelian vortices and discuss their relevance to the confinement in QCD. Finally, calculation by Douglas and Shenker of the tension ratios for vortices of different N-alities in the softly broken N=2 supersymmetric SU(N) Yang-Mills theory, is carried to the second order in the adjoint multiplet mass. A correction to the ratios violating the sine formula is found, showing that the latter is not a universal quantity.Comment: Latex 19 pages, 3 figures, Talk at Continuous Advance in QCD (Arkady Fest), Minneapolis, May 200

Who Confines Quarks? - On Non-Abelian Monopoles and Dynamics of Confinement

The role non-Abelian magnetic monopoles play in the dynamics of confinement is discussed by examining carefully a class of supersymmetric gauge theories as theoretical laboratories. In particular, in the so-called $r$-vacua of softly broken ${N}=2$ supersymmmetric $SU(n_c)$ QCD, the Goddard-Olive-Nuyts-Weinberg monopoles appear as the dominant low-energy effective degrees of freedom. Even more interesting is the physics of confining vacua which are deformations of nontrivial superconformal theories. We argue that in such cases, occurring in the $r= {n_f \over 2}$ vacua of $SU(n_c)$ theories or in all of confining vacua of $USp(2n_c)$ or $SO(n_f)$ theories with massless flavors, a new mechanism of confinement involving strongly interacting non-Abelian magnetic monopoles is at work.Comment: Latex 19 pages, 8 eps figures, uses ws-procs9x6.cls, Talk at SCGT (Nagoya, Nov. 2002) and at Institute of Physics Meeting (London, Feb. 2003

Quantum Nonabelian Monopoles

We discuss quantum mechanical and topological aspects of nonabelian monopoles. Related recent results on nonabelian vortices are also mentioned.Comment: Latex 13 pages, 2 figures, Talk at "Continuous Advances in QCD 2004", Univ. Minnesota, May 200

Revival of Non-Abelian Monopoles and Confinement in QCD

Central role played by certain non-Abelian monopoles (of Goddard-Nuyts-Olive-Weinberg type) in the infrared dynamics in many confining vacua of softly broken ${\cal N}=2$ supersymmetric gauge theories, has recently been clarified. We discuss here the main lessons to be learned from these studies for the confinement nechanism in QCD.Comment: 3 pages, Latex with appolb.cls, Contribution to Festschrift in honor of Jan Kwiecinsk

Avalanche in the Valley (Fermions, Anomaly and Unitarity in High-Energy Electroweak Interactions)

Problems related to fermions, unitarity and chiral anomaly in high energy electroweak interactions, are investigated. Particular attention is paid to the correct functional integration over fermion fields in the background of instanton-anti\-instanton type configurations. This leads to an expansion of correlation functions in terms of a small parameter, $\rho/R$, when the instanton-antiinstanton separation ($R$) is large compared to their sizes ($\rho$). Applying such a method to widely discussed cases of fermion-number violation in the electroweak theory, we conclude that there are no theoretical basis for expecting anomalous cross sections to become observable at energies in the $10$ TeV region.Comment: 11 pages + 1 figure (not included

Estimating Economic Health Costs of Not Controlling Toxic Water Pollution

The purpose of this paper is to determine what types of information may be important in determining the welfare benefits of preventing toxic water contamination when a given type of toxification occurs (or is likely to occur) in a given setting. It attempts to identify information and behavior issues that need to be considered when policy makers and others wish to obtain reasonable estimates of welfare benefits and weigh them against the economic costs of removing toxins. This paper also provides reasonable "scenarios" for three toxic pollutants that are found in water bodies (surface water or groundwater). We make use of two country alternatives--one in developing countries and the other in developed countries--to demonstrate, with specific examples of arsenic, mercury and atrazine, how welfare estimates may vary when a particular behavioral/informational scenario or a particular type of chemical contamination occurs.welfare costs, arsenic, mercury, Atrazine, information, water, Environmental Economics and Policy, Health Economics and Policy,

Coincidence between transcriptome analyses on different microarray platforms using a parametric framework

A parametric framework for the analysis of transcriptome data is demonstrated to yield coincident results when applied to data acquired using two different microarray platforms. Discrepancies among transcriptome studies are frequently reported, casting doubt on the reliability of collected data. The inconsistency among observations can be largely attributed to differences among the analytical frameworks employed for data analysis. The existing frameworks normalizes data against a standard determined from the data to be analyzed. In the present study, a parametric framework based on a strict model for normalization is applied to data acquired using an in-house printed chip and GeneChip. The framework is based on a common statistical characteristic of microarray data, and each data is normalized on the basis of a linear relationship with this model. In the proposed framework, the expressional changes observed and genes selected are coincident between platforms, achieving superior universality of data compared to other methods

Renormalization Group and Dynamics of Supersymmetric Gauge Theories

We discuss questions related to renormalization group and to nonperturbative aspects of non-Abelian gauge theories with N=2 and/or N=1 supersymmetry. Results on perturbative and nonperturbative $\beta$ functions of these theories are reviewed, and new mechanisms of confinement and dynamical symmetry breaking recently found in a class of $SU(n_c)$, $USp(2n_c)$ and $SO(n_c)$ theories are discussed.Comment: 13 pages, 3 figures, uses ws-p9-75x6-50.cls. Lecture given at the Second Conference on the ERG, Rome 200

New Results on Non-Abelian Vortices - further insights into monopole, vortex and confinement

We discuss some of the latest results concerning the non-Abelian vortices. The first concerns the construction of non-Abelian BPS vortices based on general gauge groups of the form G= G' x U(1). In particular detailed results about the vortex moduli space have been obtained for G'=SO(N) or USp(2N). The second result is about the "fractional vortices", i.e., vortices of the minimum winding but having substructures in the tension (or flux) density in the transverse plane. Thirdly, we discuss briefly the monopole-vortex complex.Comment: Latex 20 page