Conformal anomaly from gauge fields without gauge fixing

We show how the Weyl anomaly generated by gauge fields, can be computed from manifestly gauge invariant and diffeomorphism invariant exact renormalization group equations, without having to fix the gauge at any stage. Regularisation is provided by covariant higher derivatives and by embedding the Maxwell field into a spontaneously broken $U(1|1)$ supergauge theory. We first provide a realisation that leaves behind two versions of the original $U(1)$ gauge field, and then construct a manifestly $U(1|1)$ supergauge invariant flow equation which leaves behind only the original Maxwell field in the spontaneously broken regime.Comment: 24 page

Scheme Independence to all Loops

The immense freedom in the construction of Exact Renormalization Groups means that the many non-universal details of the formalism need never be exactly specified, instead satisfying only general constraints. In the context of a manifestly gauge invariant Exact Renormalization Group for SU(N) Yang-Mills, we outline a proof that, to all orders in perturbation theory, all explicit dependence of beta function coefficients on both the seed action and details of the covariantization cancels out. Further, we speculate that, within the infinite number of renormalization schemes implicit within our approach, the perturbative beta function depends only on the universal details of the setup, to all orders.Comment: 18 pages, 8 figures; Proceedings of Renormalization Group 2005, Helsinki, Finland, 30th August - 3 September 2005. v2: Published in jphysa; minor changes / refinements; refs. adde

N=1* model superpotential revisited (IR behaviour of N=4 limit)

The one-loop contribution to the superpotential, in particular the Veneziano-Yankielowicz potential in N=1 supersymmetric Yang-Mills model is discussed from an elementary field theory method and the matrix model point of view. Both approaches are based on the Renormalization Group variation of the superconformal N=4 supersymmetric Yang-Mills model.Comment: 31 page

Teaching the Universal Language of Creativity: A Guide to Training.

Teaching the Universal Language of Creativity: A Guide to Training. The purpose of education in any regard is to provide knowledge and information, to teach something. Parents, educators, and professionals alike are experiencing some difficulty in education, in that they are not being properly taught how to nurture some particular needs of individuals with developmental disabilities, specifically on how to use creativity to do so. Educators, parents, and professionals in the field need to start advocating for a balance between strict regulations and creativity. In the recent years, there has been quite the push for creativity and innovation in businesses, nationally and internationally, so where is the same push for education? This project examines creativity, in a scholarly sense, since its beginning, as well as new standards placed in public school systems, specifically in Buffalo, NY, that seem to stifle creativity. Using interviews and short survey results, the project examines and presents a curriculum to incorporate creativity into educating those who interact with individuals with developmental disabilities on a regular basis. Keywords: creativity, education, special education, developmental disabilities, Common Core, International Center for Studies in Creativity, curriculum

Sensitivity of Nonrenormalizable Trajectories to the Bare Scale

Working in scalar field theory, we consider RG trajectories which correspond to nonrenormalizable theories, in the Wilsonian sense. An interesting question to ask of such trajectories is, given some fixed starting point in parameter space, how the effective action at the effective scale, Lambda, changes as the bare scale (and hence the duration of the flow down to Lambda) is changed. When the effective action satisfies Polchinski's version of the Exact Renormalization Group equation, we prove, directly from the path integral, that the dependence of the effective action on the bare scale, keeping the interaction part of the bare action fixed, is given by an equation of the same form as the Polchinski equation but with a kernel of the opposite sign. We then investigate whether similar equations exist for various generalizations of the Polchinski equation. Using nonperturbative, diagrammatic arguments we find that an action can always be constructed which satisfies the Polchinski-like equation under variation of the bare scale. For the family of flow equations in which the field is renormalized, but the blocking functional is the simplest allowed, this action is essentially identified with the effective action at Lambda = 0. This does not seem to hold for more elaborate generalizations.Comment: v1: 23 pages, 5 figures, v2: intro extended, refs added, published in jphy

Green Fluorescent Protein in the sea urchin: new experimental approaches to transcriptional regulatory analysis in embryos and larvae

The use of Green Fluorescent Protein (GFP) as a reporter for expression transgenes opens the way to several new experimental strategies for the study of gene regulation in sea urchin development. A GFP coding sequence was associated with three different previously studied cis-regulatory systems, viz those of the SM50 gene, expressed in skeletogenic mesenchyme, the CyIIa gene, expressed in archenteron, skeletogenic and secondary mesenchyme, and the Endo16 gene, expressed in vegetal plate, archenteron and midgut. We demonstrate that the sensitivity with which expression can be detected is equal to or greater than that of whole-mount in situ hybridization applied to detection of CAT mRNA synthesized under the control of the same cis-regulatory systems. However, in addition to the important feature that it can be visualized nondestructively in living embryos, GFP has other advantages. First, it freely diffuses even within fine cytoplasmic cables, and thus reveals connections between cells, which in sea urchin embryos is particularly useful for observations on regulatory systems that operate in the syncytial skeletogenic mesenchyme. Second, GFP expression can be dramatically visualized in postembryonic larval tissues. This brings postembryonic larval developmental processes for the first time within the easy range of gene transfer analyses. Third, GFP permits identification and segregation of embryos in which the clonal incorporation of injected DNA has occurred in any particular desired region of the embryo. Thus, we show explicitly that, as expected, GFP transgenes are incorporated in the same nuclei together with other transgenes with which they are co-injected

N=1* model and glueball superpotential from Renormalization-Group-improved perturbation theory

A method for computing the low-energy non-perturbative properties of SUSY GFT, starting from the microscopic lagrangian model, is presented. The method relies on covariant SUSY Feynman graph techniques, adapted to low energy, and Renormalization-Group-improved perturbation theory. We apply the method to calculate the glueball superpotential in N=1 SU(2) SYM and obtain a potential of the Veneziano-Yankielowicz type.Comment: 19 pages, no figures; added references; note added at the end of the paper; version to appear in JHE

Parameterisation of the chemical effects of sprites in the middle atmosphere

Transient luminous events, such as red sprites, occur in the middle atmosphere in the electric field above thunderstorms. We here address the question whether these processes may be a significant source of odd nitrogen and affect ozone or other important trace species. A well-established coupled ion-neutral chemical model has been extended for this purpose and applied together with estimated rates of ionisation, excitation and dissociation based on spectroscopic ratios from ISUAL on FORMOSAT-2. This approach is used to estimate the NO<sub>x</sub> and ozone changes for two type cases. <br><br> The NO<sub>x</sub> enhancements are at most one order of magnitude in the streamers, which means a production of at most 10 mol per event, or (given a global rate of occurrence of three events per minute) some 150–1500 kg per day. The present study therefore indicates that sprites are insignificant as a global source of NO<sub>x</sub>. Local effects on ozone are also negligible, but the local enhancement of NO<sub>x</sub> may be significant, up to 5 times the minimum background at 70 km in extraordinary cases