Aspects of Integrability in Gauge/String Correspondence

In this thesis, we present our work about some generalisations of ideas, techniques and physical interpretations typical for integrable models to one of the most outstanding advances in theoretical physics of nowadays: the AdS/CFT correspondences. We have undertaken the problem of testing this conjectured duality under various points of view, but with a clear starting point - the integrability - and with a clear ambitious task in mind: to study the finite-size effects in the energy spectrum of certain string solutions on a side and in the anomalous dimensions of the gauge theory on the other. Of course, the final desire woul be the exact comparison between these two faces of the gauge/string duality. In few words, the original part of this work consists in application of well known integrability technologies, in large parte borrowed by the study of relativistic (1+1)-dimensional integrable quantum field theories, to the highly non-relativisic and much complicated case of the thoeries involved in the recent conjectures of AdS5/CFT4 and AdS4/CFT3 corrspondences. In details, exploiting the spin chain nature of the dilatation operator of N = 4 Super-Yang-Mills theory, we concentrated our attention on one of the most important sector, namely the SL(2) sector - which is also very intersting for the QCD understanding - by formulating a new type of nonlinear integral equation (NLIE) based on a previously guessed asymptotic Bethe Ansatz. The solutions of this Bethe Ansatz are characterised by the length L of the correspondent spin chain and by the number s of its excitations. A NLIE allows one, at least in principle, to make analytical and numerical calculations for arbitrary values of these parameters. The results have been rather exciting. In the important regime of high Lorentz spin, the NLIE clarifies how it reduces to a linear integral equations which governs the subleading order in s, o(s0). This also holds in the regime with L ! 1, L/ ln s finite (long operators case). This region of parameters has been particularly investigated in literature especially because of an intriguing limit into the O(6) sigma model defined on the string side. One of the most powerful methods to keep under control the finite-size spectrum of an integrable relativistic theory is the so called thermodynamic Bethe Ansatz (TBA). We proposed a highly non-trivial generalisation of this technique to the non-relativistic case of AdS5/CFT4 and made the first steps in order to determine its full spectrum - of energies for the AdS side, of anomalous dimensions for the CFT one - at any values of the coupling constant and of the size. At the leading order in the size parameter, the calculation of the finite-size corrections is much simpler and does not necessitate the TBA. It consists in deriving for a nonrelativistc case a method, invented for the first time by L¨uscher to compute the finite-size effects on the mass spectrum of relativisic theories. So, we have formulated a new version of this approach to adapt it to the case of recently found classical string solutions on AdS4 × CP3, inside the new conjecture of an AdS4/CFT3 correspondence. Our results in part confirm the string and algebraic curve calculations, in part are completely new and then could be better understood by the rapidly evolving developments of this extremely exciting research field.

Vegetables biofortified with iodine: chemical, agronomic and qualitative aspects of raw and fried potatoes

Iodine is an essential microelement for human health because it is a constituent of the thyroid hormones that regulate growth and development of the organism. Iodine Deficiency Disorders (IDDs) are believed to be one of the commonest preventable human health problems in the world today, according to the World Health Organization: that diseases include endemic goiter, cretinism and fetal abnormalities, among others, and they are caused by lack of iodine in the diet, that is the main source of iodine. Since iodine intake from food is not enough respect to human needs, this can be remedied through dietary diversification, mineral supplementation, food fortification, or increasing the concentration and/or bioavailability of mineral elements in the edible portions of crops through agricultural intervention or genetic selection (biofortification). The introduction of iodized salt is a strategy widely used and accepted to eradicate iodine deficiency, because it is an inexpensive source of stable iodine. Since the intake of salt, though iodized, must still be limited according to the risk of cardiovascular disease, so the increase of iodine content in plants for the production of functional foods is representing a field of study of particular interest and a potential market. In Italy potatoes enriched with iodine are produced by a patented procedure of agronomic biofortification for the fresh market since several years, furthermore they are recently accepted and recommended by Italian Thyroid Association, as an alternative source of iodine. Researches performed during the PhD course intended to characterize this innovative vegetables products, focusing the attention on different aspects, such as chemistry, agriculture, and quality of fresh and fried potatoes. For this purpose, lipid fraction of raw material was firstly investigated, in order to assess whether the presence of iodine in plant metabolism can affect fatty acid or sterol biosynthesis, according to the hypothesis that iodine can be bounded to polyunsaturated fatty acids of cell membranes, protecting them from peroxydation; phytosterols of plant sterol are also studied because their importance in reducing serum cholesterol, especially in potato plant sterols are also involved in synthesis of glycoalkaloid, a family of steroidal toxic secondary metabolites present in plants of the Solanaceae family. To achieve this goal chromatographic analytical techniques were employed to identify and quantify fatty acids and sterols profile of common and iodine enriched row potatoes. Another aim of the project was to evaluate the effects of frying on the quality of iodine-enriched and common potatoes. Since iodine-enriched potatoes are nowadays produced only for the fresh market, preliminary trials of cultivation under controlled environment were carried out to verify if potato varieties suitable for processing were able to absorb and accumulate iodine in the tuber. In a successive phase, these varieties were grown in the field, to evaluate their potential productivity and quality at harvest and after storage. The best potato variety to be destined for processing purposes, was finally subjected to repeated frying cycles; the effects of lipid oxidation on the composition and quality of both potatoes and frying oil bath were evaluated by chromatographic and spectrophotometric analytical techniques. Special attention were paid on volatile compounds of fried potatoes.

Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Molecular basis of Osteoarthritis and aspects of cellular senescence in disease

The aim of this study is to investigate on some molecular mechanisms contributing to the pathogenesis of osteoarthritis (OA) and in particular to the senescence of articular chondrocytes. It is focused on understanding molecular events downstream GSK3β inactivation or dependent on the activity of IKKα, a kinase that does not belong to the phenotype of healthy articular chondrocytes. Moreover, the potential of some nutraceuticals on scavenging ROS thus reducing oxidative stress, DNA damage, and chondrocyte senescence has been evaluated in vitro. The in vitro LiCl-mediated GSK3β inactivation resulted in increased mitochondrial ROS production, that impacted on cellular proliferation, with S-phase transient arrest, increased SA-β gal and PAS staining, cell size and granularity. ROS are also responsible for the of increased expression of two major oxidative lesions, i.e. 1) double strand breaks, tagged by γH2AX, that associates with activation of GADD45β and p21, and 2) 8-oxo-dG adducts, that associate with increased IKKα and MMP-10 expression. The pattern observed in vitro was confirmed on cartilage from OA patients. IKKa dramatically affects the intensity of the DNA damage response induced by oxidative stress (H2O2 exposure) in chondrocytes, as evidenced by silencing strategies. At early time point an higher percentage of γH2AX positive cells and more foci in IKKa-KD cells are observed, but IKKa KD cells proved to almost completely recover after 24 hours respect to their controls. Telomere attrition is also reduced in IKKaKD. Finally MSH6 and MLH1 genes are up-regulated in IKKαKD cells but not in control cells. Hydroxytyrosol and Spermidine have a great ROS scavenging capacity in vitro. Both treatments revert the H2O2 dependent increase of cell death and γH2AX-foci formation and senescence, suggesting the ability of increasing cell homeostasis. These data indicate that nutraceuticals represent a great challenge in OA management, for both therapeutical and preventive purposes.