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.

Pretrattamenti termo-meccanici ed enzimatici su scarti dell'industria enologica per la produzione di Biogas

A fundamental assumption for by-product from winery industy waste-management is their economic and commercial increase in value. High energetic value recovery from winery industry is an attractive economic solution to stimulate new sustainable process. Approach of this work is based about physic and biological treatment with grape stalks and grape marc to increase polysaccharides components of cell wall and energetic availability of this by-products. Grape stalks for example have a high percentage of lignin and cellulose and can’t be used, whitout pretreatment, for an anaerobic digestion process. Our findings show enzymatic and thermo-mechanical pre-treatments in combined application for optimise hydrolytic mechanism on winemaking wastes which represents 0,9 milion ton/year in Italy and on straw, cereal by-products with high lignin content. A screening of specifically industrial enzymatic complex for the hydrolysis lignocellulosic biomass were tested using the principal polysaccharides component of the vegetal cells. Combined thermo-mechanical and enzymatic pretreatment improve substrates conversion in batch test fermentation experiment. The conservation of the grape stalks, at temperature above 0°C, allow the growth of spontaneus fermentation that reduce their polysaccharides content so had investigated anarobic condition of conservation. The other objective of this study was to investigate the capability of a proprietary strain of L.buchneri LN 40177 to enhance the accessibility of fermentable forage constituents during the anaerobic conservation process by releasing the enzyme ferulate esterase. The time sequence study by batch tests showed that the L. buchneri LN-40177 inoculated grape stalk substrate was more readily available in the fermenter. In batch tests with grape stalk, after mechanical treatment, the L. buchneri LN41077 treated substrate yielded on average 70% more biogas per kg/DM. Thermo-mechanical, enzymatic and biological treatment with L. buchneri LN-40177 can increase the biogas production from low fermented biomasses and the consequent their useful in anaerobic biodigesters for agro-bioenergy production.