Exact Correlators from Conformal Ward Identities in Momentum Space and the Perturbative TJJTJJ Vertex

We present a general study of 3-point functions of conformal field theory in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWI' s), introduced in recent works by Bzowski, McFadden and Skenderis (BMS). We investigate and detail the structure of the CWI's, their non-perturbative solutions and the transition to momentum space, comparing them to perturbation theory by taking QED as an example. We then proceed with an analysis of the $TJJ$ correlator, presenting independent and detailed re-derivations of the conformal equations in the reconstruction method of BMS, originally formulated using a minimal tensor basis in the transverse traceless sector. A careful comparison with a second basis introduced in previous studies shows that this correlator is affected by one anomaly pole in the graviton (T) line, induced by renormalization. The result shows that the origin of the anomaly, in this correlator, should be necessarily attributed to the exchange of a massless effective degree of freedom. Our results are then exemplified in massless QED at one-loop in $d$-dimensions, expressed in terms of perturbative master integrals. An independent analysis of the Fuchsian character of the solutions, which bypasses the 3K integrals, is also presented. We show that the combination of field theories at one-loop - with a specific field content of degenerate massless scalar and fermions - is sufficient to generate the complete non-perturbative solution, in agreement with a previous study in coordinate space. The result shows that free conformal field theories, in specific dimensions, arrested at one-loop, reproduce the general result for the $TJJ$. Analytical checks of this correspondence are presented in $d=3,4$ and $5$ spacetime dimensions[..].Comment: 79 pages, 3 Figures. Final version, with changes in section 8. Accepted for publication in Nuclear Physics

Conformal Ward Identities and the Coupling of QED and QCD to Gravity

We present a general study of 3-point functions of conformal field theory (CFT) in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWIs), introduced in recent works. We investigate and detail the structure of the CWIs and their non-perturbative solutions, and compare them to perturbation theory, taking QED and QCD as examples. Exact solutions of CFT's in the flat background limit in momentum space are matched by the perturbative realizations in free field theories, showing that the origin the conformal anomaly is related to efffective scalar interactions, generated by the renormalization of the longitudinal components of the corresponding operators.Comment: 5 pages. Proceedings of the Workshop QCD@work 2018, 25-28 June 2018, Matera, Ital

The Generalized Hypergeometric Structure of the Ward Identities of CFT's in Momentum Space in d>2d > 2

We review the emergence of hypergeometric structures (of $F_4$ Appell functions) from the conformal Ward identities (CWIs) in conformal field theories (CFTs) in dimensions $d > 2$. We illustrate the case of scalar 3- and 4-point functions. 3-point functions are associated to hypergeometric systems with 4 independent solutions. For symmetric correlators they can be expressed in terms of a single 3K integral - functions of quadratic ratios of momenta - which is a parametric integral of three modified Bessel $K$ functions. In the case of scalar 4-point functions, by requiring the correlator to be conformal invariant in coordinate space as well as in some dual variables (i.e. dual conformal invariant), its explicit expression is also given by a 3K integral, or as a linear combination of Appell functions which are now quartic ratios of momenta. Similar expressions have been obtained in the past in the computation of an infinite class of planar ladder (Feynman) diagrams in perturbation theory, which, however, do not share the same (dual conformal/conformal) symmetry of our solutions. We then discuss some hypergeometric functions of 3 variables, which define 8 particular solutions of the CWIs and correspond to Lauricella functions. They can also be combined in terms of 4K integral and appear in an asymptotic description of the scalar 4-point function, in special kinematical limits.Comment: 31 pages, 1 figure. Invited contribution to appear in: Axioms (MDPI) "Geometric Analysis and Mathematical Physics" Ed. Sorin Dragomir, revised final version, typos correcte

Exact Correlators from Conformal Ward Identities in Momentum Space and Perturbative Realizations

The general solution of the conformal Ward identities (CWI's) in momentum space, and their matching to perturbation theory, allows to uncover some specific characteristics of the breaking of conformal symmetry, induced by the anomaly. It allows to compare perturbative features of the 1-particle irreducible (1PI, nonlocal) anomaly action with the prediction of a similar (but exact) nonlocal action identified by the CWI's. The two predictions can be exactly matched at the level of 3-point functions. The analysis of the $TJJ$ and $TTT$ shows that both approaches - based either on 1PI or on the exact solutions of the CWI's - predict massless (dynamical) scalar exchanges in 3-point functions as the signature of the conformal anomaly. In a local formulation such 1PI actions exhibit a ghost in the spectrum which may induce ghost condensation. We also discuss alternative approaches, which take to Wess-Zumino forms of the action with an asymptotic dilaton, which should be considered phenomenological alternatives to the exact nonlocal action. If derived by a Weyl gauging, they also include a ghost in the spectrum. The two formulations, nonlocal and of WZ type, can be unified under the assumption that they describe the same anomaly phenomenon at two separate (UV/IR) ends of the renormalization group flow, possibly separated by a vacuum rearrangement at an intermediate scale. A similar analysis is presented for an $\mathcal{N}=1$ supersymmetric Yang-Mills theory. We comment on the possibile cosmological implications of such quasi Nambu-Goldstone modes as ultralight dilatons and axions.Comment: 48 pages, 12 figures, (typos corrected) Proceedings of the Corfu Summer Institute 2018 "School and Workshops on Elementary Particle Physics and Gravity" 1-27 September 2018 Corfu, Greec

Progetto e storia: il caso di Rodi

International audienceL'organismo urbano di Rodi custodisce un'eredità storico-architettonica piuttosto ricca, dovuta al succedersi di diverse dominazioni portatrici ciascuna di una propria politica urbana. L'articolo propone uno studio dell'organismo urbano di Rodi attraverso la lettura tipo-morfologica delle fasi evolutive della città, dei suoi elementi tipici-atipici, delle sue polarità e dei suoi percorsi a partire dal periodo bizantino fino alla dominazione ottomana. Una lettura a partire dalle stratificazioni urbane più recenti si rivela importante non solo per la comprensione della città antica ma anche in vista dell'attuazione di interventi progettuali più consapevoli, siano essi azioni sull'esistente o progetti del nuovo. Entrambi, infatti, devono saldarsi alla realtà urbana preesistente ed inserirsi come ultimo passaggio di un processo di appropriazione della storia del sito attraverso la lettura delle sue fasi urbane, e proporsi come momenti operativi di conoscenza

Compte rendu du livre M. Tuchscherer, M.P. Pedani, Alexandrie ottomane 1. Etudes Alexandrines 19, Institut Français d'Archéologie Orientale, Le Caire 2011

Compte rendu d'un ouvrage scientifique pour le site Histara-SorbonneL'ouvrage fait partie d'un programme de recherche autour de la ville ottomane (XVIe-XVIIIe s.), afin d'apporter un éclairage nouveau sur la période médiévale et la ville actuelle. L'ouvrage porte sur la présentation de deux sources : le firman de Soliman le Magnifique pour la Nation française d'Alexandrie (1528) et les Relazioni des consuls vénitiens dans la ville, pour la plupart inédites (1554-1664). Les préalables historiques dans l'ouvrage fournissent un appui synthétique et complet, toutefois il n'y a pas une conclusion faisant le point sur les contenus et sur les pistes de recherche possibles, ainsi que sur l'utilité spécifique de ces sources pour la reconstruction de la ville turque et de ses relations politiques, économiques et culturelles. À mon avis, enfin, le projet de l'ouvrage est intéressant par rapport à la reprise récente des études sur les réseaux marchands et diplomatiques en Méditerranée, ainsi qu'à l'appauvrissement général des ports méditerranéens face à l'ouverture de la " voie atlantique " pendant la période moderne

Gli architetti tedeschi e la Sizilienreise nell’Ottocento

Nel corso del XIX secolo il viaggio in Sicilia degli architetti tedeschi vede mutare obiettivi, modalità e percorsi. Dal viaggio fondativo di Goethe, attento ad aspetti naturalistici, artistici e socio-antropologici, ma comunque centrato sulle tappe della classicità già a partire dal soggiorno di Karl Friedrich Schinkel nel 1804, si amplia la gamma dei possibili interessi. Alla ricerca di novità e “curiosità”, l’architetto prussiano considera l’itinerario classico un elemento acquisito e si appassiona in maniera più decisa agli esempi da lui definiti “saraceni” e agli episodi di architettura rurale. Il viaggio di Schinkel influenza le esperienze delle generazioni successive di architetti, non solo suoi allievi: basti citare i casi di Friedrich August Stüler, accompagnato da Eduard Knoblauch a distanza di vent’anni dal viaggio del maestro, e di Johan Heinrich Strack, in Sicilia nel 1838 e forse anche nel 1854, quando accompagna lungo la penisola il principe Friedrich di Hohenzollern. Gli interessi sono già mutati rispetto a quelli del maestro prussiano e per Strack la classicità si riversa in un sincretico ideale neorinascimentale. Parallelamente a tali esperienze si svolgono quelle di Jakob Ignaz Hittorff e Leo von Klenze, entrambi in Sicilia tra il 1823 e il 1824. Il lavoro di Klenze, che accompagna Ludwig di Baviera, è da un lato finalizzato alla ricerca di progetti per i futuri cantieri d’oltralpe, come quelli per il Walhalla di Ratisbona e per la Allerheiligenhofkirche a Monaco, ma dall’altro rappresenta uno studio quasi archeologico dei monumenti antichi. In concorrenza con Klenze, Hittorff lavora a Selinunte, contribuendo alla decisiva scoperta del colore ed entrando in dibattito che vede coinvolti inglesi, francesi e tedeschi, tra cui anche Schinkel stesso e Gottfried Semper. Il filone della policromia trova proprio nelle “scoperte” siciliane la propria radice iniziale, poi corroborata dagli studi, effettuati tra gli altri proprio da Semper, anche a Pompei. Ovviamente anche gli studi sull’architettura medievale non possono prescindere dall’analisi degli esempi siciliani. In qualche modo già Schinkel aveva puntato l’attenzione su epoche ancora considerate di decadenza, ma i suoi allievi presentano uno sguardo più consapevole ed una diversa prospettiva storica. Se la Cappella Palatina fornisce numerose suggestioni, come avviene per Ludwig di Baviera e Leo von Klenze, lo studio di Heinrich Wilhelm Schulz si focalizza proprio sui grandi capolavori del medioevo, e segnatamente del romanico. Peraltro, tali studi sono condotti operando un continuo confronto con gli studiosi siciliani, da sempre capaci di interloquire in maniera fruttuosa con la cultura germanica. Il rapporto tra la Sicilia e gli architetti tedeschi muta notevolmente nel corso dei decenni, ma informa una serie di riflessioni decisive per comprendere il corso degli eventi in ambito tedesco. La scoperta del sud trova un completamento solo con la tappa siciliana, una considerazione che a maggior ragione vale per quanti sono alla ricerca di modelli classici e arabo-normanni, ma anche per chi voglia assicurarsi una formazione completa e ricca

Tower-mansions of Crete. A multidisciplinary approach to learn built heritage

As part of a research on Venetian and Ottoman architecture in Crete, this paper introduces a first inventory of fortified mansions and tower-houses. They formed a network controlling coasts, plains, and cultivated lands. It is hard to retrace the origin of these houses without deploying stratigraphic and chemical analysis. However, a first morphological study has identified recurring elements: a small plan with several floors and an access on the first level; embrasures, bretèches and putlog holes, as well as a fireplace; and a decorative sobriety. In a surveyed tower-house we find that military devices refer to a first constructive phase, while residential elements refer to a second phase. These hybrid features are common to fortified houses in the Mediterranean and beyond, which were strong elements of military and spatial organization. This vernacular and colonial heritage has got a significant value in terms of architectural models and possible reuse

The changing role of historic town of Rhodes in the scenario of Ottoman and Italian rules in the light of the iconographic sources

International audienceRhodes was the Hospitaller stronghold until the early modern age. It went through an urban and architectural evolution under the Ottoman and Italian rules. Iconography until the twentieth century shows the search for medieval souvenirs in the Islamic town, the creation of a travel destination and the shifting of the symbolic-geographic idea of city, linked to a new attitude towards built heritage. We will trace the changing role of the historic town in Turkish and Italian ideology and practice

Exploratory analysis of the relationships among different methods of assessing adherence and glycemic control in youth with type 1 diabetes mellitus

Objectives: The present study examined four methods of assessing diabetes adherence (self-report, diary measure, electronic monitoring, and provider rating) within a population of youth with Type I Diabetes Mellitus (T1DM). Methods: Comparisons were conducted among the four methods of assessing diabetes adherence. Associations among the seven different measures of blood glucose monitoring (BGM) and HbA1c were examined. An exploratory stepwise regression analysis was conducted to determine the best predictors of glycemic control (i.e., Hemoglobin A1c; HbA1c) while controlling for relevant demographic variables. Results: The adherence measures appeared to be interrelated. The relationships between many of the BGM measures and HbA1c demonstrated a medium effect size. The Self Care Inventory (SCI) adjusted global score was the strongest predictor of HbA1c, even after taking the demographic variables into account. Conclusions: The SCI is a robust, easy-to-use, and cost-efficient measure of adherence that has a strong relationship to HbA1c. Demographic variables are important to examine within the context of different methods of assessing adherence. The research methodology utilized to assess both general diabetes adherence and more specific behavioral measurements of BGM should be clearly documented in future studies to ensure accurate interpretation of results. (PsycINFO Database Record (c) 2011 APA, all rights reserved