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.

Automatic code generation: from process algebraic architectural descriptions to multithreaded java programs

Process algebraic architectural description languages provide a formal means for modeling software systems and assessing their properties. In order to bridge the gap between system modeling and system im- plementation, in this thesis an approach is proposed for automatically generating multithreaded object-oriented code from process algebraic architectural descriptions, in a way that preserves – under certain assumptions – the properties proved at the architectural level. The approach is divided into three phases, which are illustrated by means of a running example based on an audio processing system. First, we develop an architecture-driven technique for thread coordination management, which is completely automated through a suitable package. Second, we address the translation of the algebraically-specified behavior of the individual software units into thread templates, which will have to be filled in by the software developer according to certain guidelines. Third, we discuss performance issues related to the suitability of synthesizing monitors rather than threads from software unit descriptions that satisfy specific constraints. In addition to the running example, we present two case studies about a video animation repainting system and the implementation of a leader election algorithm, in order to summarize the whole approach. The outcome of this thesis is the implementation of the proposed approach in a translator called PADL2Java and its integration in the architecture-centric verification tool TwoTowers.

Economy and environment: Issues on transport externalities, CO2 responsibility and environmental Kuznets curve

In this thesis some of the most important issues presently debated on international sustainability are analysed. The thesis is composed of five independent studies that tackle organically the following issues: the maritime transport externalities, the environmental Kuznets curve, the responsibilities in the carbon dioxide emissions and the integrated approach that have to be used to translate the principles of sustainability into policy. The analysis will be instrumental to demonstrating that sustainability, being a matter of economy, society and environment, requires to be analysed in a transdisciplinary perspective. Using an integrated approach to analyse the relationships between economy and environment, this thesis highlight that sustainability management requires joint economic instruments, integrated analysis, societal behavioural changes as well as responsibilities shifting.