Dressing and Wrapping

We prove that the validity of the recently proposed dressed, asymptotic Bethe ansatz for the planar AdS/CFT system is indeed limited at weak coupling by operator wrapping effects. This is done by comparing the Bethe ansatz predictions for the four-loop anomalous dimension of finite-spin twist-two operators to BFKL constraints from high-energy scattering amplitudes in N=4 gauge theory. We find disagreement, which means that the ansatz breaks down for length-two operators at four-loop order. Our method supplies precision tools for multiple all-loop tests of the veracity of any yet-to-be constructed set of exact spectral equations. Finally we present a conjecture for the exact four-loop anomalous dimension of the family of twist-two operators, which includes the Konishi field.Comment: 20 pages, 2 tables, no figures; v2: references added, conjecture on exact four-loop twist-two result state

Bethe equations for generalized Hubbard models

We compute the eigenfunctions, energies and Bethe equations for a class of generalized integrable Hubbard models based on gl(n|m)\oplus gl(2) superalgebras. The Bethe equations appear to be similar to the Hubbard model ones, up to a phase due to the integration of a subset of `simple' Bethe equations. We discuss relations with AdS/CFT correspondence, and with condensed matter physics.Comment: 36 page

On the commuting charges for the highest dimension SU(2) operators in planar N=4{\cal N}=4 SYM

We consider the highest anomalous dimension operator in the SU(2) sector of planar ${\cal N}=4$ SYM at all-loop, though neglecting wrapping contributions. In any case, the latter enter the loop expansion only after a precise length-depending order. In the thermodynamic limit we write both a linear integral equation for the Bethe root density and a linear system obeyed by the commuting charges. Consequently, we determine the leading strong coupling contribution to the density and from this an approximation to the leading and sub-leading terms of any charge $Q_r$: it scales as $\lambda ^{1/4-r/2}$, which generalises the Gubser-Klebanov-Polyakov energy law. In the end, we briefly extend these considerations to finite lengths and 'excited' operators by using the idea of a non-linear integral equation.Comment: Latex file, 20 pages, some typos corrected, some technical details expanded and explaine

Aspects of Integrability in N =4 SYM

Various recently developed connections between supersymmetric Yang-Mills theories in four dimensions and two dimensional integrable systems serve as crucial ingredients in improving our understanding of the AdS/CFT correspondence. In this review, we highlight some connections between superconformal four dimensional Yang-Mills theory and various integrable systems. In particular, we focus on the role of Yangian symmetries in studying the gauge theory dual of closed string excitations. We also briefly review how the gauge theory connects to Calogero models and open quantum spin chains through the study of the gauge theory duals of D3 branes and open strings ending on them. This invited review, written for Modern Physics Letters-A, is based on a seminar given at the Institute of Advanced Study, Princeton.Comment: Invited brief review for Mod. Phys. Lett. A based on a talk at I.A.S, Princeto

Group 1 and group 2 metal complexes supported by a bidentate bulky iminopyrrolyl ligand: synthesis, structural diversity, and ε-caprolactone polymerization study

We report here a series of alkali and alkaline earth metal complexes, each with a bulky iminopyrrolyl ligand [2-(Ph3CN[double bond, length as m-dash]CH)C4H3NH] (1-H) moiety in their coordination sphere, synthesized using either alkane elimination or silylamine elimination methods or the salt metathesis route. The lithium salt of molecular composition [Li(2-(Ph3CN[double bond, length as m-dash]CH)C4H3N)(THF)2] (2) was prepared using the alkane elimination method, and the silylamine elimination method was used to synthesize the dimeric sodium and tetra-nuclear potassium salts of composition [(2-(Ph3CN[double bond, length as m-dash]CH)C4H3N)Na(THF)]2 (3) and [(2-(Ph3CN[double bond, length as m-dash]CH)C4H3N)K(THF)0.5]4 (4) respectively. The magnesium complex of composition [(THF)2Mg(CH2Ph){2-(Ph3CN[double bond, length as m-dash]CH)C4H3N}] (5) was synthesized through the alkane elimination method, in which [Mg(CH2Ph)2(OEt2)2] was treated with the bulky iminopyrrole ligand 1-H in 1 : 1 molar ratio, whereas the bis(iminopyrrolyl)magnesium complex [(THF)2Mg{2-(Ph3CN[double bond, length as m-dash]CH)C4H3N}2] (6) was isolated using the salt metathesis route. The heavier alkaline earth metal complexes of the general formula {(THF)nM(2-(Ph3CN[double bond, length as m-dash]CH)C4H3N)2} [M = Ca (7), Sr (8), and n = 2; M = Ba (9), n = 3] were prepared in pure form using two synthetic methods: in the first method, the bulky iminopyrrole ligand 1-H was directly treated with the alkaline earth metal precursor [M{N(SiMe3)2}2(THF)n] (where M = Ca, Sr and Ba) in 2 : 1 molar ratio in THF solvent at ambient temperature. The complexes 7–9 were also obtained using the salt metathesis reaction, which involves the treatment of the potassium salt (4) with the corresponding metal diiodides MI2 (M = Ca, Sr and Ba) in 2 : 1 molar ratio in THF solvent. The molecular structures of all the metal complexes (1-H, 2–9) in the solid state were established through single-crystal X-ray diffraction analysis. The complexes 5–9 were tested as catalysts for the ring-opening polymerization of ε-caprolactone. High activity was observed in the heavier alkaline earth metal complexes 7–9, with a very narrow polydispersity index in comparison to that of magnesium complexes 5 and 6

Non-responsive coeliac disease : a comprehensive review from the NHS England national centre for refractory coeliac disease

Coeliac disease is a common small intestinal enteropathy which manifests following ingestion of gluten in genetically susceptible individuals. Since gluten was identified as the driving factor in coeliac disease, the gluten-free diet (GFD) has remained the mainstay of treatment. While most individuals will display improvement in symptoms and signs of coeliac disease following institution of the GFD, up to 30% will continue to experience symptoms and/or have persisting intestinal inflammation. These individuals can be classified as having non-responsive coeliac disease (NRCD), which may be associated with dietary indiscretion, slow healing, refractory coeliac disease, and/or an alternative condition. The purpose of this review is to provide an overview of the causes of NRCD in adults, highlight a systematic approach to investigate these patients, and appraise the latest management aspects of this subset of coeliac disease

THE ADAPTIVE RESPONSE AND PROTECTION AGAINST HERITABLE MUTATIONS AND FETAL MALFORMATION

There are a number of studies that show radiation can cause heritable mutations in the offspring of irradiated organisms. These “germ-line mutations” have been shown to occur in unique sequences of DNA called “minisatellite loci”. The high frequencies of spontaneous and induced mutations at minisatellite loci allow mutation induction to be measured at low doses of exposure in a small population, making minisatellite mutation a powerful tool to investigate radiation-induced heritable mutations. However, the biological significance of these mutations is uncertain, and their relationship to health risk or population fitness is unknown. We have adopted this mutation assay to study the role of adaptive response in protecting mice against radiation-induced heritable defects. We have shown that male mice, adapted to radiation with a low dose priming exposure, do not pass on mutations to their offspring caused by a subsequent large radiation exposure to the adapted males. This presentation and paper provide a general overview of radiationinduced mutations in offspring and explain the effect of low dose exposures and the adaptive response on these mutations. It is also known that exposure of pregnant females to high doses of radiation can cause death or malformation (teratogenesis) in developing fetuses. Malformation can only occur during a specialized stage of organ formation known as organogenesis. Studies in rodents show that radiation-induced fetal death and malformation can be significantly reduced when a pregnant female is exposed to a prior low dose of ionizing radiation. The mechanism of this protective effect, through an adaptive response, depends on the stage of organogenesis when the low dose exposures are delivered. To better understand this process, we have investigated the role of an important gene known as p53. Therefore, this report will also discuss fetal effects of ionizing radiation and explain the critical stages of development when fetuses are at risk. Research will be explained that investigates the biological and genetic systems (p53) that protect the developing fetus and discuss the role of low dose radiation adaptive response in these processes

Review of AdS/CFT Integrability, Chapter I.3: Long-range spin chains

In this contribution we briefly review recent developments in the theory of long-range integrable spin chains. These spin chains constitute a natural generalisation of the well-studied integrable nearest-neighbour chains and are of particular relevance to the integrability in the AdS/CFT correspondence since the dilatation operator in the asymptotic region is conjectured to be a Hamiltonian of an integrable long-range psu spin chain.Comment: 17 pages, see also overview article arXiv:1012.3982, v2: references to other chapters updated, v3: minor typos corrected, references adde