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.

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.

Physiological and Biochemical Aspects of Iron Nutrition in Grapevine

The objective of this thesis was to study the response mechanisms of grapevine to Fe-deficiency and to potential Fe chlorosis prevention strategies. The results show that the presence of bicarbonate in the nutrient solution shifted the activity of PEPC and TCA cycle enzymes and the accumulation/translocation of organic acids in roots of Fe-deprived plants. The rootstock 140 Ruggeri displayed a typical behavior of calcicole plants under bicarbonate stress. The Fe chlorosis susceptible rootstock 101-14 reacted to a prolonged Fe-deficiency reducing the root activity of PEPC and MDH. Noteworthy, it accumulates high levels of citric acid in roots, indicating a low capacity to utilizing, transporting and/or exudating organic acids into the rhizosfere. In contrast, 110 Richter rootstock is capable to maintain an active metabolism of organic acids in roots, accumulating them to a lesser extent than 101-14. Similarly to 101-14, SO4 genotype displays a strong decrease of mechanisms associated to Fe chlorosis tolerance (PEPC and MDH enzymes). Nevertheless it is able to avoid excessive accumulation of citric acid in roots, similar as 110 Richter rootstock. Intercropping with Festuca rubra increased leaf chlorophyll content and net photosynthesis. In addition, intercropping reduces the activity of PEPC in roots, similary to Fe-chelate supply. Applications of NH4+ with nitrification inhibitor prevents efficiently Fe-deficiency, increases chlorophyll content, and induces similar root biochemical responses as Fe-EDDHA. Without the addition of nitrification inhibitors, the effectiveness of NH4+ supply on Fe chlorosis prevention resulted significantly lower. The aspects intertwined in this investigation highlight the complexity of Fe physiology and the fine metabolic tuning of grapevine genotypes to Fe availability and soil-related environmental factors. The experimental evidences reveal the need to carry out future researches on Fe nutrition maintaining a continous flow of knowledge between theoretical and agronomical perspectives for fully supporting the efforts devoted to convert science into practice.

From core rigidities to dynamic capabilities: the role of external knowledge. A multiple case study

This study focuses on the processes of change that firms undertake to overcome conditions of organizational rigidity and develop new dynamic capabilities, thanks to the contribution of external knowledge. When external contingencies highlight firms’ core rigidities, external actors can intervene in change projects, providing new competences to firms’ managers. Knowledge transfer and organizational learning processes can lead to the development of new dynamic capabilities. Existing literature does not completely explain how these processes develop and how external knowledge providers, as management consultants, influence them. Dynamic capabilities literature has become very rich in the last years; however, the models that explain how dynamic capabilities evolve are not particularly investigated. Adopting a qualitative approach, this research proposes four relevant case studies in which external actors introduce new knowledge within organizations, activating processes of change. Each case study consists of a management consulting project. Data are collected through in-depth interviews with consultants and managers. A large amount of documents supports evidences from interviews. A narrative approach is adopted to account for change processes and a synthetic approach is proposed to compare case studies along relevant dimensions. This study presents a model of capabilities evolution, supported by empirical evidence, to explain how external knowledge intervenes in capabilities evolution processes: first, external actors solve gaps between environmental demands and firms’ capabilities, changing organizational structures and routines; second, a knowledge transfer between consultants and managers leads to the creation of new ordinary capabilities; third, managers can develop new dynamic capabilities through a deliberate learning process that internalizes new tacit knowledge from consultants. After the end of the consulting project, two elements can influence the deliberate learning process: new external contingencies and changes in the perceptions about external actors.

Poverty and Mental Health. Tangible and Intangible Aspects of Microcredit

Microcredit, a small lending system, invests on an individual's creativity by stimulating the development of their own potential. This process leads to the attainment of various objectives which in turn allow individuals to develop their skill awareness. Consequently, this process also increases an individual’s self-esteem and self-confidence. These factors play an important role in the aetiology of a number of mental disorders. Namely, those characterized by a series of psychological conditions which impede the full development of a person’s personal, relational and social sphere. Furthermore, since Microcredit is thought to produce tangible goods, such as income, and intangible goods, such as self-esteem and mutual trust, it could also represent an innovative socio-economic tool. We therefore also hypothesize that, Microcredit would be valuable in maximizing abilities/skills in those subjects who are financially excluded and rarely perceived as a ‘resource’ for the Community The longitudinal study set the impact of the Grameen Bank microcredit program on new borrowers women from Noakhali District at the south Bangladesh. The impact evaluation assessment has been structured to detect individual, family and social changes. Manova Analysis allowed distinguishing from women with positive or negative outcomes related to the loan performance. Data revealed consistent differences in terms of economical outcomes and psychological well being amongst the groups of subject analyzed. The data gathered in relation to the changes arisen in the individuals should be looked into through future, continuous and systematic, monitoring.