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.

Quantum Integrability in Non-Linear Sigma Models related to Gauge/String Correspondences

The Thermodynamic Bethe Ansatz analysis is carried out for the extended-CP^N class of integrable 2-dimensional Non-Linear Sigma Models related to the low energy limit of the AdS_4xCP^3 type IIA superstring theory. The principal aim of this program is to obtain further non-perturbative consistency check to the S-matrix proposed to describe the scattering processes between the fundamental excitations of the theory by analyzing the structure of the Renormalization Group flow. As a noteworthy byproduct we eventually obtain a novel class of TBA models which fits in the known classification but with several important differences. The TBA framework allows the evaluation of some exact quantities related to the conformal UV limit of the model: effective central charge, conformal dimension of the perturbing operator and field content of the underlying CFT. The knowledge of this physical quantities has led to the possibility of conjecturing a perturbed CFT realization of the integrable models in terms of coset Kac-Moody CFT. The set of numerical tools and programs developed ad hoc to solve the problem at hand is also discussed in some detail with references to the code.

Aldo Rossi, autobiografia scientifica: scrittura come progetto. Indagine critica tra scrittura e progetto di architettura

«In altri termini mi sfuggiva e ancora oggi mi sfugge gran parte del significato dell’evoluzione del tempo; come se il tempo fosse una materia che osservo dall’esterno. Questa mancanza di evoluzione è fonte di alcune mie sventure ma anche mi appartiene con gioia.» Aldo Rossi, Autobiografia scientifica. The temporal dimension underpinning the draft of Autobiografia scientifica by Aldo Rossi may be referred to what Lucien Lévy-Bruhl, the well-known French anthropologist, defines as “primitive mentality” and “prelogical” conscience : the book of life has lost its page numbers, even punctuation. For Lévy-Bruhl, but certainly for Rossi, life or its summing up becomes a continuous account of ellipses, gaps, repetitions that may be read from left to right or viceversa, from head to foot or viceversa without distinction. Rossi’s autobiographical writing seems to accept and support the confusion with which memories have been collected, recording them after the order memory gives them in the mental distillation or simply according to the chronological order in which they have happened. For Rossi, the confusion reflects the melting of memory elements into a composite image which is the result of a fusion. He is aware that the same sap pervades all memories he is going to put in order: each of them has got a common denominator. Differences have diminished, almost faded; the quick glance is prevalent over the distinction of each episode. Rossi’s writing is beyond the categories dependent on time: past and present, before and now. For Rossi, the only repetition – the repetition the text will make possible for an indefinite number of times – gives peculiarity to the event. As Gilles Deleuze knows, “things” may only last as “singleness”: more frequent the repetition is, more singular is the memory phenomenon that recurs, because only what is singular magnifies itself and happens endlessly forever. Rossi understands that “to raise the first time to nth forever”, repetition becomes glorification . It may be an autobiography that, celebrating the originality, enhances the memory event in the repetition; in fact it greatly differs from the biographical reproduction, in which each repetition is but a weaker echo, a duller copy, provided with a smaller an smaller power in comparison with the original. Paradoxically, for Deleuze the repetition asserts the originality and singularity of what is repeated. Rossi seems to share the thought expressed by Kierkegaard in the essay Repetition: «The hope is a graceful maiden slipping through your fingers; the memory of an elderly woman, indeed pretty, but never satisfactory if necessary; the repetition is a loved friend you are never tired of, as it is only the new to make you bored. The old never bores you and its presence makes you happy [...] life is but a repetition [...] here is the beauty of life» . Rossi knows well that repetition hints at the lasting stability of cosmic time. Kierkegaard goes on: «The world exists, and it exists as a repetition» . Rossi devotes himself, on purpose and in all conscience, to collect, to inventory and «to review life», his own life, according to a recovery not from the past but of the past: a search work, the «recherche du temps perdu», as Proust entitled his masterpiece on memory. If you want the past time to be not wasted, you must give it presence. «Memoria e specifico come caratteristiche per riconoscere se stesso e ciò che è estraneo mi sembravano le più chiare condizioni e spiegazioni della realtà. Non esiste uno specifico senza memoria, e una memoria che non provenga da un momento specifico; e solo questa unione permette la conoscenza della propria individualità e del contrario (self e non-self)» . Rossi wants to understand himself, his own character; it is really his own character that requires to be understood, to increase its own introspective ability and intelligence. «Può sembrare strano che Planck e Dante associno la loro ricerca scientifica e autobiografica con la morte; una morte che è in qualche modo continuazione di energia. In realtà, in ogni artista o tecnico, il principio della continuazione dell’energia si mescola con la ricerca della felicità e della morte» . The eschatological incipit of Rossi’s autobiography refers to Freud’s thought in the exact circularity of Dante’s framework and in as much exact circularity of the statement of the principle of the conservation of energy: in fact it was Freud to connect repetition to death. For Freud, the desire of repetition is an instinct rooted in biology. The primary aim of such an instinct would be to restore a previous condition, so that the repeated history represents a part of the past (even if concealed) and, relieving the removal, reduces anguish and tension. So, Freud ask himself, what is the most remote state to which the instinct, through the repetition, wants to go back? It is a pre-vital condition, inorganic of the pure entropy, a not-to-be condition in which doesn’t exist any tension; in other words, Death. Rossi, with the theme of death, introduces the theme of circularity which further on refers to the sense of continuity in transformation or, in the opposite way, the transformation in continuity. «[...] la descrizione e il rilievo delle forme antiche permettevano una continuità altrimenti irripetibile, permettevano anche una trasformazione, una volta che la vita fosse fermata in forme precise» . Rossi’s attitude seems to hint at the reflection on time and – in a broad sense – at the thought on life and things expressed by T.S. Eliot in Four Quartets: «Time present and time past / Are both perhaps present in time future, / And time future is contained in time past. / I all time is eternally present / All time is unredeemable. / What might have been is an abstraction / Remaining perpetual possibility / Only in a word of speculation. / What might have been and what has been / Point to one end, which is always present. [...]» . Aldo Rossi’s autobiographical story coincides with the description of “things” and the description of himself through the things in the exact parallel with craft or art. He seems to get all things made by man to coincide with the personal or artistic story, with the consequent immediate necessity of formulating a new interpretation: the flow of things has never met a total stop; all that exists nowadays is but a repetition or a variant of something existing some time ago and so on, without any interruption until the early dawnings of human life. Nevertheless, Rossi must operate specific subdivisions inside the continuous connection in time – of his time – even if limited by a present beginning and end of his own existence. This artist, as an “historian” of himself and his own life – as an auto-biographer – enjoys the privilege to be able to decide if and how to operate the cutting in a certain point rather than in another one, without being compelled to justify his choice. In this sense, his story is a matter very ductile and flexible: a good story-teller can choose any moment to start a certain sequence of events. Yet, Rossi is aware that, beyond the mere narration, there is the problem to identify in history - his own personal story – those flakings where a clean cut enables the separation of events of different nature. In order to do it, he has to make not only an inventory of his own “things”, but also to appeal to authority of the Divina Commedia started by Dante when he was 30. «A trent’anni si deve compiere o iniziare qualcosa di definitivo e fare i conti con la propria formazione» . For Rossi, the poet performs his authority not only in the text, but also in his will of setting out on a mystical journey and handing it down through an exact descriptive will. Rossi turns not only to the authority of poetry, but also evokes the authority of science with Max Plank and his Scientific Autobiography, published, in Italian translation, by Einaudi, 1956. Concerning Planck, Rossi resumes an element seemingly secondary in hit account where the German physicist «[...] risale alle scoperte della fisica moderna ritrovando l’impressione che gli fece l’enunciazione del principio di conservazione dell’energia; [...]» . It is again the act of describing that links Rossi to Planck, it is the description of a circularity, the one of conservation of energy, which endorses Rossi’s autobiographical speech looking for both happiness and death. Rossi seems to agree perfectly to the thought of Planck at the opening of his own autobiography: «The decision to devote myself to science was a direct consequence of a discovery which was never ceased to arouse my enthusiasm since my early youth: the laws of human thought coincide with the ones governing the sequences of the impressions we receive from the world surrounding us, so that the mere logic can enable us to penetrate into the latter one’s mechanism. It is essential that the outer world is something independent of man, something absolute. The search of the laws dealing with this absolute seems to me the highest scientific aim in life» . For Rossi the survey of his own life represents a way to change the events into experiences, to concentrate the emotion and group them in meaningful plots: «It seems, as one becomes older. / That the past has another pattern, and ceases to be a mere sequence [...]» Eliot wrote in Four Quartet, which are a meditation on time, old age and memory . And he goes on: «We had the experience but missed the meaning, / And approach to the meaning restores the experience / In a different form, beyond any meaning [...]» . Rossi restores in his autobiography – but not only in it – the most ancient sense of memory, aware that for at least 15 centuries the Latin word memoria was used to show the activity of bringing back images to mind: the psychology of memory, which starts with Aristotele (De Anima), used to consider such a faculty totally essential to mind. Keith Basso writes: «The thought materializes in the form of “images”» . Rossi knows well – as Aristotele said – that if you do not have a collection of mental images to remember – imagination – there is no thought at all. According to this psychological tradition, what today we conventionally call “memory” is but a way of imagining created by time. Rossi, entering consciously this stream of thought, passing through the Renaissance ars memoriae to reach us gives a great importance to the word and assumes it as a real place, much more than a recollection, even more than a production and an emotional elaboration of images.

Supramolecular functional assemblies with photo or chemical addressability

Supramolecular self-assembly represents a key technology for the spontaneous construction of nanoarchitectures and for the fabrication of materials with enhanced physical and chemical properties. In addition, a significant asset of supramolecular self-assemblies rests on their reversible formation, thanks to the kinetic lability of their non-covalent interactions. This dynamic nature can be exploited for the development of “self-healing” and “smart” materials towards the tuning of their functional properties upon various external factors. One particular intriguing objective in the field is to reach a high level of control over the shape and size of the supramolecular architectures, in order to produce well-defined functional nanostructures by rational design. In this direction, many investigations have been pursued toward the construction of self-assembled objects from numerous low-molecular weight scaffolds, for instance by exploiting multiple directional hydrogen-bonding interactions. In particular, nucleobases have been used as supramolecular synthons as a result of their efficiency to code for non-covalent interaction motifs. Among nucleobases, guanine represents the most versatile one, because of its different H-bond donor and acceptor sites which display self-complementary patterns of interactions. Interestingly, and depending on the environmental conditions, guanosine derivatives can form various types of structures. Most of the supramolecular architectures reported in this Thesis from guanosine derivatives require the presence of a cation which stabilizes, via dipole-ion interactions, the macrocyclic G-quartet that can, in turn, stack in columnar G-quadruplex arrangements. In addition, in absence of cations, guanosine can polymerize via hydrogen bonding to give a variety of supramolecular networks including linear ribbons. This complex supramolecular behavior confers to the guanine-guanine interactions their upper interest among all the homonucleobases studied. They have been subjected to intense investigations in various areas ranging from structural biology and medicinal chemistry – guanine-rich sequences are abundant in telomeric ends of chromosomes and promoter regions of DNA, and are capable of forming G-quartet based structures– to material science and nanotechnology. This Thesis, organized into five Chapters, describes mainly some recent advances in the form and function provided by self-assembly of guanine based systems. More generally, Chapter 4 will focus on the construction of supramolecular self-assemblies whose self-assembling process and self-assembled architectures can be controlled by light as external stimulus. Chapter 1 will describe some of the many recent studies of G-quartets in the general area of nanoscience. Natural G- quadruplexes can be useful motifs to build new structures and biomaterials such as self-assembled nanomachines, biosensors, therapeutic aptamer and catalysts. In Chapters 2-4 it is pointed out the core concept held in this PhD Thesis, i.e. the supramolecular organization of lipophilic guanosine derivatives with photo or chemical addressability. Chapter 2 will mainly focus on the use of cation-templated guanosine derivatives as a potential scaffold for designing functional materials with tailored physical properties, showing a new way to control the bottom-up realization of well-defined nanoarchitectures. In section 2.6.7, the self-assembly properties of compound 28a may be considered an example of open-shell moieties ordered by a supramolecular guanosine architecture showing a new (magnetic) property. Chapter 3 will report on ribbon-like structures, supramolecular architectures formed by guanosine derivatives that may be of interest for the fabrication of molecular nanowires within the framework of future molecular electronic applications. In section 3.4 we investigate the supramolecular polymerizations of derivatives dG 1 and G 30 by light scattering technique and TEM experiments. The obtained data reveal the presence of several levels of organization due to the hierarchical self-assembly of the guanosine units in ribbons that in turn aggregate in fibrillar or lamellar soft structures. The elucidation of these structures furnishes an explanation to the physical behaviour of guanosine units which display organogelator properties. Chapter 4 will describe photoresponsive self-assembling systems. Numerous research examples have demonstrated that the use of photochromic molecules in supramolecular self-assemblies is the most reasonable method to noninvasively manipulate their degree of aggregation and supramolecular architectures. In section 4.4 we report on the photocontrolled self-assembly of modified guanosine nucleobase E-42: by the introduction of a photoactive moiety at C8 it is possible to operate a photocontrol over the self-assembly of the molecule, where the existence of G-quartets can be alternately switched on and off. In section 4.5 we focus on the use of cyclodextrins as photoresponsive host-guest assemblies: αCD–azobenzene conjugates 47-48 (section 4.5.3) are synthesized in order to obtain a photoresponsive system exhibiting a fine photocontrollable degree of aggregation and self-assembled architecture. Finally, Chapter 5 contains the experimental protocols used for the research described in Chapters 2-4.

Studi sull'epigramma scoptico greco

The dissertation is divided into two parts: the first synthesis focused on the definition of the epigram scoptico imperial age, the second analysis concerns the study of the minor poets of Book XI. In the Introduction (I), the attention focuses on the genesis of imperial scoptic epigram: here you try to draw a picture of the satirical Greek literature before the middle of the century AD to identify the debts of the scoptic epigram, especially Lucillius’, in respect of previous authors (from the Middle-up comedy to epigrams of the Crown of Philip), and to emphasize the remoteness of this literary phenomenon from other experiences of ironic and satirical poetry (Catullus). In the chapter on the Themes (II), the study was limited to professional groups and those most targeted (doctors, grammarians, etc..), to that particular type represented by the satire on ethnic groups. The study of minor poets is necessarily preceded by a general discussion on the authors most representative of the greek satiric poetry: Lucillius, Ammianus, Nicarchus and Palladas (III). All the minor poets of the eleventh book, which you can not provide a date, have been regarded by scholars as the ‘poets of Diogenian’: the chapter on Anthologion of Diogenian (IV), which is undergoing critical to the existence (assumed but never proven) of the lost source of Book XI, therefore, serves as an introduction to the commentary of the authors required minors. During the discussion they are not qualified as poets ‘poets of Diogenian’, but are divided into two categories: those included in the string of alphabetically ordered AP XI 388-436 (V), and those who are not part of (VI). Finally, a separate chapter (VII) is devoted to the age-old question of epigrams assigned to Lucian, both in the string of alphabetically ordered epigrams, as well as outside it.

Strong semiclassical gravity in the universe and the laboratory

Three published papers are resumed in this thesis. Different aspects of the semiclassical theory of gravity are discussed. In chapter 1 we find a new perturbative (yet analytical) solution to the unsolved problem of the metric junction between two Friedmann-Robertson-Walker using Israel's formalism. The case of an expanding radiation core inside an expanding or collapsing dust exterior is treated. This model can be useful in the "landscape" cosmology in string theory or for treating new gravastar configurations. In chapter 2 we investigate the possible use of the Kodama vector field as a substitute for the Killing vector field. In particular we find the response function of an Unruh detector following an (accelerated) Kodama trajectory. The detector has finite extension and backreaction is considered. In chapter 3 we study the possible creation of microscopic black holes at LHC in the brane world model. It is found that the black hole tidal charge has a fundamental role in preventing the formation of the horizon.

On the GKP Vacuum in Gauge/Gravity Correspondences

Within the framework of the AdS5/CFT4 correspondence, the GKP string living on a AdS5 x S5 background finds a counterpart in the anti-ferromagnetic vacuum state for the spin chain, fruitfully employed to investigate the dual N=4 SYM superconformal gauge theory. The thesis mainly deals with the excitations over such a vacuum: dispersion relations and scattering matrices are computed, moreover a set of Asymptotic Bethe Ansatz equations is formulated. Furthermore, the survey of the GKP vacuum within the AdS4/CFT3 duality between a string theory on AdS4 x CP 3 and N=6 Chern-Simons reveals intriguing connections relating the latter to N=4 SYM, in a peculiar high spin limit.

Lipophilic nucleosides: studies toward self-assembled functional materials

Molecular self-assembly takes advantage of supramolecular non-covalent interactions (ionic, hydrophobic, van der Waals, hydrogen and coordination bonds) for the construction of organized and tunable systems. In this field, lipophilic guanosines can represent powerful building blocks thanks to their aggregation proprieties in organic solvents, which can be controlled by addition or removal of cations. For example, potassium ion can template the formation of piled G-quartets structures, while in its absence ribbon-like G aggregates are generated in solution. In this thesis we explored the possibility of using guanosines as scaffolds to direct the construction of ordered and self-assembled architectures, one of the main goals of bottom-up approach in nanotechnology. In Chapter III we will describe Langmuir-Blodgett films obtained from guanosines and other lipophilic nucleosides, revealing the “special” behavior of guanine in comparison with the other nucleobases. In Chapter IV we will report the synthesis of several thiophene-functionalized guanosines and the studies towards their possible use in organic electronics: the pre-programmed organization of terthiophene residues in ribbon aggregates could allow charge conduction through π-π stacked oligothiophene functionalities. The construction and the behavior of some simple electronic nanodevices based on these organized thiopehene-guanosine hybrids has been explored.