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.

The stratigraphic record of the quaternary sea level fluctuations and the impact of the post-glacial sea level rise (Termination I) in the Adriatic basin (Mediterranean sea)

The modern stratigraphy of clastic continental margins is the result of the interaction between several geological processes acting on different time scales, among which sea level oscillations, sediment supply fluctuations and local tectonics are the main mechanisms. During the past three years my PhD was focused on understanding the impact of each of these process in the deposition of the central and northern Adriatic sedimentary successions, with the aim of reconstructing and quantifying the Late Quaternary eustatic fluctuations. In the last few decades, several Authors tried to quantify past eustatic fluctuations through the analysis of direct sea level indicators, among which drowned barrier-island deposits or coral reefs, or indirect methods, such as Oxygen isotope ratios (δ18O) or modeling simulations. Sea level curves, obtained from direct sea level indicators, record a composite signal, formed by the contribution of the global eustatic change and regional factors, as tectonic processes or glacial-isostatic rebound effects: the eustatic signal has to be obtained by removing the contribution of these other mechanisms. To obtain the most realistic sea level reconstructions it is important to quantify the tectonic regime of the central Adriatic margin. This result has been achieved integrating a numerical approach with the analysis of high-resolution seismic profiles. In detail, the subsidence trend obtained from the geohistory analysis and the backstripping of the borehole PRAD1.2 (the borehole PRAD1.2 is a 71 m continuous borehole drilled in -185 m of water depth, south of the Mid Adriatic Deep - MAD - during the European Project PROMESS 1, Profile Across Mediterranean Sedimentary Systems, Part 1), has been confirmed by the analysis of lowstand paleoshorelines and by benthic foraminifera associations investigated through the borehole. This work showed an evolution from inner-shelf environment, during Marine Isotopic Stage (MIS) 10, to upper-slope conditions, during MIS 2. Once the tectonic regime of the central Adriatic margin has been constrained, it is possible to investigate the impact of sea level and sediment supply fluctuations on the deposition of the Late Pleistocene-Holocene transgressive deposits. The Adriatic transgressive record (TST - Transgressive Systems Tract) is formed by three correlative sedimentary bodies, deposited in less then 14 kyr since the Last Glacial Maximum (LGM); in particular: along the central Adriatic shelf and in the adjacent slope basin the TST is formed by marine units, while along the northern Adriatic shelf the TST is represented by costal deposits in a backstepping configuration. The central Adriatic margin, characterized by a thick transgressive sedimentary succession, is the ideal site to investigate the impact of late Pleistocene climatic and eustatic fluctuations, among which Meltwater Pulses 1A and 1B and the Younger Dryas cold event. The central Adriatic TST is formed by a tripartite deposit bounded by two regional unconformities. In particular, the middle TST unit includes two prograding wedges, deposited in the interval between the two Meltwater Pulse events, as highlighted by several 14C age estimates, and likely recorded the Younger Dryas cold interval. Modeling simulations, obtained with the two coupled models HydroTrend 3.0 and 2D-Sedflux 1.0C (developed by the Community Surface Dynamics Modeling System - CSDMS), integrated by the analysis of high resolution seismic profiles and core samples, indicate that: 1 - the prograding middle TST unit, deposited during the Younger Dryas, was formed as a consequence of an increase in sediment flux, likely connected to a decline in vegetation cover in the catchment area due to the establishment of sub glacial arid conditions; 2 - the two-stage prograding geometry was the consequence of a sea level still-stand (or possibly a fall) during the Younger Dryas event. The northern Adriatic margin, characterized by a broad and gentle shelf (350 km wide with a low angle plunge of 0.02° to the SE), is the ideal site to quantify the timing of each steps of the post LGM sea level rise. The modern shelf is characterized by sandy deposits of barrier-island systems in a backstepping configuration, showing younger ages at progressively shallower depths, which recorded the step-wise nature of the last sea level rise. The age-depth model, obtained by dated samples of basal peat layers, is in good agreement with previous published sea level curves, and highlights the post-glacial eustatic trend. The interval corresponding to the Younger Dyas cold reversal, instead, is more complex: two coeval coastal deposits characterize the northern Adriatic shelf at very different water depths. Several explanations and different models can be attempted to explain this conundrum, but the problem remains still unsolved.

The special rights other than shares in cross-border mergers of limited liability companies within the European Union. A perspective from the Spanish Law

The present research aims to study the special rights other than shares in Spanish Law and the protection of their holders in cross-border mergers of limited liability companies within the European Union frame. Special rights other than shares are recognised as an independent legal category within legal systems of some EU Member States, such as Germany or Spain, through the implementation of the Third Directive 78/855/CEE concerning mergers of public limited liability companies. The above-cited Directive contains a special regime of protection for the holders of securities, other than shares, to which special rights are attached, consisting of being given rights in the acquiring company, at least equivalent to those they possessed in the company being acquired. This safeguard is to highlight the intimate connection between this type of rights and the company whose extinction determines the existence of those. Pursuant to the Directive 2005/56/CE on cross-border mergers of limited liability companies, each company taking part in these operations shall comply with the safeguards of members and third parties provided in their respective national law to which is subject. In this regard, the protection for holders of special rights other than shares shall be ruled by the domestic M&A regime. As far as Spanish Law are concerned, holders of these special rights are recognized a right of merger information, in the same terms as shareholders, as well as equal rights in the company resulting from the cross-border merger. However, these measures are not enough guarantee for a suitable protection, thus considering those holders of special rights as special creditors, sometimes it will be necessary to go to the general protection regime for creditors. In Spanish Law, it would involve the recognition of right to the merger opposition, whose exercise would prevent the operation was completed until ensuring equal rights.

Perturbative and non perturbative effects in the Standard Model and orbifolded ADS/CFT based theories

We study some perturbative and nonperturbative effects in the framework of the Standard Model of particle physics. In particular we consider the time dependence of the Higgs vacuum expectation value given by the dynamics of the StandardModel and study the non-adiabatic production of both bosons and fermions, which is intrinsically non-perturbative. In theHartree approximation, we analyze the general expressions that describe the dissipative dynamics due to the backreaction of the produced particles. Then, we solve numerically some relevant cases for the Standard Model phenomenology in the regime of relatively small oscillations of the Higgs vacuum expectation value (vev). As perturbative effects, we consider the leading logarithmic resummation in small Bjorken x QCD, concentrating ourselves on the Nc dependence of the Green functions associated to reggeized gluons. Here the eigenvalues of the BKP kernel for states of more than three reggeized gluons are unknown in general, contrary to the large Nc limit (planar limit) case where the problem becomes integrable. In this contest we consider a 4-gluon kernel for a finite number of colors and define some simple toy models for the configuration space dynamics, which are directly solvable with group theoretical methods. In particular we study the depencence of the spectrum of thesemodelswith respect to the number of colors andmake comparisons with the planar limit case. In the final part we move on the study of theories beyond the Standard Model, considering models built on AdS5 S5/Γ orbifold compactifications of the type IIB superstring, where Γ is the abelian group Zn. We present an appealing three family N = 0 SUSY model with n = 7 for the order of the orbifolding group. This result in a modified Pati–Salam Model which reduced to the StandardModel after symmetry breaking and has interesting phenomenological consequences for LHC.

I limiti all'autonomia procedurale degli Stati membri dell'UE in materia risarcitoria

This work analyses the limits that the principle of State liability for damages suffered by individuals because of breach of EU law poses to the procedural autonomy of the Member States of the EU. The introductory part of this work is dedicated to the general character of the limitations EU law poses to the State’s competence in procedural matters. The first part of the research, instead, focuses on the specific limits that european law poses on the rules of procedure related to the legal regime of the right to compensation and its operating conditions; in particular, this first part explores respectively the “substantive” and “procedural” limits that EU law poses to the State’s autonomy to regulate actions for damages for breaches of EU law. The substantial limits concern the conditions of eligibility of liability and the constitutive conditions of the right to compensation; the procedural limits to the action for damages refer to the concrete organization and characteristics of the judicial action. The second part of the research is devoted to rules of procedure governing the relations between judicial remedies explicitly aimed at protecting the right to reparation and other remedies that may be relevant, both europeans and nationals. The first chapter of the second part of this work focuses on the rules governing the relations between the action for damages brought up at the national level and the remedies provided by european Treaties; finally, I explore the relations between the action for damages brought up at the national level and other remedies present in the same national juridical order. I reconstruct all the limits to the procedural autonomy of Member States concerning the right to compensation; consequently, I verify that those limits represent part of the system of internal procedures, able to guarantee the respect of european law.

Fra il nome e la storia. Trasformazioni del discorso politico e concetto di classe al principio della monarchia di Luglio (1831-1832)

La ricerca indaga tensioni e trasformazioni che investono le principali correnti di pensiero politico in Francia nei primi anni della monarchia di Luglio, e vi osserva l’emergere del concetto di classe. Assumendo la dimensione dell’avvenimento come punto di intersezione fra storia e teoria, l’elaborato si concentra sul periodo novembre 1831-giugno 1832 per analizzare il modo in cui, nell’ordine del discorso politico repubblicano, liberale e socialista, le vicende di questi mesi vengono interpretate cercando di dar nome alle figure sociali che esse fanno irrompere nel dibattito pubblico. Il titolo Fra il nome e la storia fa dunque riferimento allo sforzo di indagare il campo di tensione che si apre fra concreto divenire storico e grandi operazioni di nominazione che segnano l’affiorare di strutture concettuali della lunga durata. L’emergere della nozione di classe operaia e delle categorie che intorno a essa si organizzano viene interpretata come una «formazione discorsiva» che pone in questione significato e confini del politico. La frattura del 1848 è assunta come orizzonte e margine esterno della ricerca nella misura in cui si ipotizza che essa segni una prima affermazione del regime di verità di tale formazione discorsiva: lo statuto politico del lavoro. L’elaborato consta di quattro capitoli. I primi tre indagano la riflessione sul politico e la funzione che in essa svolge il concetto di classe a partire dall’interpretazione di alcuni avvenimenti del tornante 1831-32 proposta nel discorso repubblicano del quotidiano «Le National» e della Société des Amis du Peuple, in quello del liberalismo dottrinario di François Guizot e in quello socialista nascente, prima del movimento sansimoniano, e poi muovendo fino al 1848 francese con l’analisi propostane da Karl Marx. Il quarto capitolo indaga infine la dimensione del «sociale», la sua elaborazione e articolazione attraverso il lavoro di studio e oggettivazione delle figure del mondo del lavoro.

L’interpretazione simultanea dal polacco all’italiano: le strategie per affrontare le catene nominali

La presente tesi rappresenta il primo studio dedicato all’interpretazione simultanea dal polacco all’italiano. La presente ricerca cerca di identificare il modo in cui interpreti di comprovata esperienza gestiscono alcune difficoltà tipiche della sintassi polacca fortemente divergenti da quella italiana. La scelta di studiare le catene nominali deriva dal confronto di quanto emerso dalle indagini sulla linguistica contrastiva con un’inchiesta tra gli interpreti accreditati presso le istituzioni europee per quella combinazione. Il primo capitolo è dedicato ad una panoramica sui contatti passati e presenti tra l’Italia e la Polonia e ad una riflessione sulla lingua polacca in chiave contrastiva con l’italiano. Il secondo capitolo si concentra sulla ricerca nell’ambito dell’interpretazione simultanea, in particolare sugli studi contrastivi e sulla discussione delle strategie usate dagli interpreti. Il terzo capitolo approfondisce il contesto di questo studio ovvero le istituzioni europee, il il multilinguismo e il regime linguistico al Parlamento Europeo. Il quarto capitolo include l’indagine del lavoro, condotta su un ampio corpus di dati. Sono stati infatti trascritti e analizzati tutti gli interventi tenuti in lingua polacca in occasione delle sedute parlamentari a Strasburgo e a Bruxelles del 2011 e del primo semestre 2009 e le relative interppretazioni in italiano (per un totale di oltre 9 ore di parlato per lingua). Dall’analisi è risultato che l’interprete nella maggior parte dei casi cerca, nonostante la velocità d’eloquio dell’oratore, di riprodurre fedelmente il messaggio. Tuttavia, qualora questo non risulti possibile, si è notato come gli interpreti ricorrano in maniera consapevole all’omissione di quelle informazioni desumibili o dal contesto o dalle conoscenze pregresse dell’ascoltatore. Di conseguenza la riduzione non rappresenta una strategia di emergenza ma una risorsa da applicare consapevolmente per superare le difficoltà poste da lunghe sequenze di sostantivi.

Gravitational Lensing as a Tool on Galactic and Cosmological Scales

This work considers the reconstruction of strong gravitational lenses from their observed effects on the light distribution of background sources. After reviewing the formalism of gravitational lensing and the most common and relevant lens models, new analytical results on the elliptical power law lens are presented, including new expressions for the deflection, potential, shear and magnification, which naturally lead to a fast numerical scheme for practical calculation. The main part of the thesis investigates lens reconstruction with extended sources by means of the forward reconstruction method, in which the lenses and sources are given by parametric models. The numerical realities of the problem make it necessary to find targeted optimisations for the forward method, in order to make it feasible for general applications to modern, high resolution images. The result of these optimisations is presented in the \textsc{Lensed} algorithm. Subsequently, a number of tests for general forward reconstruction methods are created to decouple the influence of sourced from lens reconstructions, in order to objectively demonstrate the constraining power of the reconstruction. The final chapters on lens reconstruction contain two sample applications of the forward method. One is the analysis of images from a strong lensing survey. Such surveys today contain $\sim 100$ strong lenses, and much larger sample sizes are expected in the future, making it necessary to quickly and reliably analyse catalogues of lenses with a fixed model. The second application deals with the opposite situation of a single observation that is to be confronted with different lens models, where the forward method allows for natural model-building. This is demonstrated using an example reconstruction of the ``Cosmic Horseshoe''. An appendix presents an independent work on the use of weak gravitational lensing to investigate theories of modified gravity which exhibit screening in the non-linear regime of structure formation.