Large N and the renormalization group

In the large N limit, we show that the Local Potential Approximation to the flow equation for the Legendre effective action, is in effect no longer an approximation, but exact - in a sense, and under conditions, that we determine precisely. We explain why the same is not true for the Polchinski or Wilson flow equations and, by deriving an exact relation between the Polchinski and Legendre effective potentials (that holds for all N), we find the correct large N limit of these flow equations. We also show that all forms (and all parts) of the renormalization group are exactly soluble in the large N limit, choosing as an example, D dimensional O(N) invariant N-component scalar field theory.Comment: 13 pages, uses harvmac; Added: one page with further clarification of the main results, discussion of earlier work, and new references. To be published in Phys. Lett.

Exact Renormalization Group Equations. An Introductory Review

We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.Comment: Final version to appear in Phys. Rep.; Many references added, section 4.2 added, minor corrections. 65 pages, 6 fig

Derivative expansion of the renormalization group in O(N) scalar field theory

We apply a derivative expansion to the Legendre effective action flow equations of O(N) symmetric scalar field theory, making no other approximation. We calculate the critical exponents eta, nu, and omega at the both the leading and second order of the expansion, associated to the three dimensional Wilson-Fisher fixed points, at various values of N. In addition, we show how the derivative expansion reproduces exactly known results, at special values N=infinity,-2,-4, ... .Comment: 29 pages including 4 eps figures, uses LaTeX, epsfig, and latexsy

Exact renormalization group flow equations for non-relativistic fermions: scaling towards the Fermi surface

We construct exact functional renormalization group (RG) flow equations for non-relativistic fermions in arbitrary dimensions, taking into account not only mode elimination but also the rescaling of the momenta, frequencies and the fermionic fields. The complete RG flow of all relevant, marginal and irrelevant couplings can be described by a system of coupled flow equations for the irreducible n-point vertices. Introducing suitable dimensionless variables, we obtain flow equations for generalized scaling functions which are continuous functions of the flow parameter, even if we consider quantities which are dominated by momenta close to the Fermi surface, such as the density-density correlation function at long wavelengths. We also show how the problem of constructing the renormalized Fermi surface can be reduced to the problem of finding the RG fixed point of the irreducible two-point vertex at vanishing momentum and frequency. We argue that only if the degrees of freedom are properly rescaled it is possible to reach scale-invariant non-Fermi liquid fixed points within a truncation of the exact RG flow equations.Comment: 20 Revtex pages, with 4 figures; final version to appear in Phys. Rev. B; references and some explanations adde

Amyloid-β nanotubes are associated with prion protein-dependent synaptotoxicity

Growing evidence suggests water-soluble, non-fibrillar forms of amyloid-β protein (Aβ) have important roles in Alzheimer's disease with toxicities mimicked by synthetic Aβ1-42. However, no defined toxic structures acting via specific receptors have been identified and roles of proposed receptors, such as prion protein (PrP), remain controversial. Here we quantify binding to PrP of Aβ1-42 after different durations of aggregation. We show PrP-binding and PrP-dependent inhibition of long-term potentiation (LTP) correlate with the presence of protofibrils. Globular oligomers bind less avidly to PrP and do not inhibit LTP, whereas fibrils inhibit LTP in a PrP-independent manner. That only certain transient Aβ assemblies cause PrP-dependent toxicity explains conflicting reports regarding the involvement of PrP in Aβ-induced impairments. We show that these protofibrils contain a defined nanotubular structure with a previously unidentified triple helical conformation. Blocking the formation of Aβ nanotubes or their interaction with PrP might have a role in treatment of Alzheimer's disease

Multi-colony tracking reveals segregation in foraging range, space use, and timing in a tropical seabird

Colonial animals experience density-dependent competition for food, which is posited to influence foraging range and lead to inter-colony segregation. However, such patterns are poorly studied in the tropics, where predictable day lengths, oligotrophic conditions, and facultative foraging may alter the relationships between foraging and intra-specific competition. Here, we GPS-tracked 207 breeding red-footed boobies Sula sula rubripes (RFB) from 4 neighbouring Chagos Archipelago colonies (~1100 to 9200 breeding pairs) in the central Indian Ocean, to determine how foraging strategies (i.e. effort, segregation, and timing) vary with colony, while accounting for sex, monsoon season, stage of reproduction, year, and individual. During incubation and chick-rearing, RFBs commute to pelagic foraging grounds (maximum distance mean ± SE: 112.9 ± 3.7 km; total distance: 298.4 ± 6.2 km) over 1 to 5 d (18.5 ± 1.6 h). Foraging effort was highest at the largest colony, and greater among females than males. Departure angles varied among colonies, leading to foraging areas that were largely spatially segregated. Timing of departures and arrivals were strongly constrained by daylight hours, although females and birds at the largest colony left earliest. Our study highlights the importance of inter-colony differences in tropical seabird foraging, which may relate to different levels of intra-specific competition. Moreover, links between foraging times and colony size suggest a previously undescribed outcome of density-dependent competition, highlighting the importance of understanding colonial living across multiple dimensions.</jats:p

Field Theory Entropy, the HH-theorem and the Renormalization Group

We consider entropy and relative entropy in Field theory and establish relevant monotonicity properties with respect to the couplings. The relative entropy in a field theory with a hierarchy of renormalization group fixed points ranks the fixed points, the lowest relative entropy being assigned to the highest multicritical point. We argue that as a consequence of a generalized $H$ theorem Wilsonian RG flows induce an increase in entropy and propose the relative entropy as the natural quantity which increases from one fixed point to another in more than two dimensions.Comment: 25 pages, plain TeX (macros included), 6 ps figures. Addition in title. Entropy of cutoff Gaussian model modified in section 4 to avoid a divergence. Therefore, last figure modified. Other minor changes to improve readability. Version to appear in Phys. Rev.

Re-emerging syphilis: a detrended correspondence analysis of the behaviour of HIV positive and negative gay men

BACKGROUND: Recent syphilis outbreaks in the UK have raised serious concerns about the sexual health of the population. Moreover, syphilis appears more likely to facilitate HIV transmission than any other sexually transmitted infection (STI). METHODS: The sexual and other risk behaviour of a sample of HIV positive and negative gay men with and without syphilis was subjected to a detrended correspondence analysis (DCA). RESULTS: A DCA plot was used to illustrate similarity of individuals in terms of their behaviours, regardless of their infection status. The majority of those with syphilis (78%; 18/23) fell into a high-risk group with more partners, and use of anonymous sex venues and drugs during sex. However, 16% of uninfected controls (8/49) and 62% of HIV positive individuals without syphilis (8/13) also fell into this high-risk group. CONCLUSIONS: Using a statistical technique that is novel for this type of investigation, we demonstrate behavioural overlaps between syphilis-infected individuals in an ongoing UK outbreak and uninfected HIV positive and negative controls. Given the high-risk behaviour of a significant proportion of uninfected individuals, ongoing transmission of syphilis and HIV in this population seems likely

Identification of a Compound That Disrupts Binding of Amyloid-β to the Prion Protein Using a Novel Fluorescence-based Assay

The prion protein (PrP) has been implicated both in prion diseases such as Creutzfeldt-Jakob disease, where its monomeric cellular isoform (PrP(C)) is recruited into pathogenic self-propagating polymers of misfolded protein, and in Alzheimer disease, where PrP(C) may act as a receptor for synaptotoxic oligomeric forms of amyloid-β (Aβ). There has been considerable interest in identification of compounds that bind to PrP(C), stabilizing its native fold and thereby acting as pharmacological chaperones to block prion propagation and pathogenesis. However, compounds binding PrP(C) could also inhibit the binding of toxic Aβ species and may have a role in treating Alzheimer disease, a highly prevalent dementia for which there are currently no disease-modifying treatments. However, the absence of a unitary, readily measurable, physiological function of PrP makes screening for ligands challenging, and the highly heterogeneous nature of Aβ oligomer preparations makes conventional competition binding assays difficult to interpret. We have therefore developed a high-throughput screen that utilizes site-specifically fluorescently labeled protein to identify compounds that bind to PrP and inhibit both Aβ binding and prion propagation. Following a screen of 1,200 approved drugs, we identified Chicago Sky Blue 6B as the first small molecule PrP ligand capable of inhibiting Aβ binding, demonstrating the feasibility of development of drugs to block this interaction. The interaction of Chicago Sky Blue 6B was characterized by isothermal titration calorimetry, and its ability to inhibit Aβ binding and reduce prion levels was established in cell-based assays

Inflammatory pathways in the mechanism of parturition

Increasing evidence suggests that parturition is an inflammatory process. In this brief overview, inflammatory events occurring in association with parturition, and the mechanism by which they may contribute to labour and delivery will be discussed. Mention will be made of how this information may be of use in regulating the timing and the onset of parturition