AREA 3. - STRING THEORY AND QUATUM GRAVITY The discovery of D-branes as non-perturbative states of string theory has opened the way to use string theory to describe the gauge theory living on their world-volume. This is possible thanks to the two-fold nature of D-branes to be, on the one hand, a classical solution of the low-energy effective action containing closed strings and, on the other one, to support a gauge theory on their world-volume due to the open strings attached to it. Supegravity solutions encode the dual gauge theory both in non-perturbative and perturbative regimes. It has been shown that quantum properties such as the chiral and scale anomalies of supersymmetric and non- conformal theories living on D-branes can be obtained from their corresponding classical supergravity solution. In particular, in previous works, a bound state of fractional D3-branes localized inside the world-volume of fractional D7-branes in the orbifolds C^2/Z_2 and C^3/(Z_2xZ_2) has been studied. For a suitable number of D3 and D7 branes and by using the corresponding supergravity solution, the super QCD N=2 and N=1 scale and chiral anomalies have been reproduced. It has been given an explanation of the beautiful working of the gauge/gravity correspondence in Type IIB superstring theory by computing the "annulus" diagram corresponding to the interaction of a fractional D3 brane with a gauge field turned-on on its world volume and a "stack" of N D3 fractional branes embedded in the orbifolds C^2/Z_2 and C^3/(Z_2xZ_2). It has been shown that the logarithmic divergence exhibited by this amplitude can be equivalently read as due to the massless open string states circulating in the loop or to the massless closed string states exchanged between the branes. This, in turn, follows from the fact that, by performing a suitable conformal transformation which sends the open into closed string (open/closed string duality), the contribution of the massless open string states is mapped into the one of the closed string states, while the contribution of the massive states (threshold corrections) is vanishing. Hence the reasons why perturbative properties of many gauge theories living on non-conformal and with reduced supersymmetry branes are reproduced from their corresponding supergravity solution lie in the open/closed string duality and in the vanishing thresholds. Activity 3.1 - string theory and gauge/gravity correspondance A. Liccardo, R. Marotta, R. Musto, F. Nicodemi, R. Pettorino, F. Pezzella It has been explored the role of supersymmetry in the working of the gauge/gravity correspondence. To this aim Type O string theory and its orientifold have been taken in exam. In so doing, it has been obtained a realization in terms of branes of the so- called "orientifold field theories". These are non supersymmetric gauge theories having the same bosonic sector as Super Yang-Mills N=4,2,1 theories according to the chosen orientifold. In particular, one of the most interesting results has been the derivation of QCD with three colours as world-volume theory of a certain brane configuration. From the analysis of such models it has been obtained the result that the gauge/gravity correspondence is not a property peculiar of supersymmetric models, as Type IIB, but it holds as well in non-supersymmetric models when, also in this case, threshold corrections vanish. It has been understood that such a condition is satisfied when the massive states in the string models taken in exam are arranged as "short" multiplets of supersymmetric gauge theories N=4. Program for 2005 A natural development of the research activity until now followed consists in establishing a connection between our results in the framework of the gauge/gravity correspondence and those one can find in literature obtained through the duality seen as a geometrical transition. In this approach gauge theories have been obtained as world-volume theories of branes wrapped on cycles of "resolved" Calabi-Yau manifolds. They admit a "dual" description in which branes disappear and are substituted by fluxes of suitable supergravity fields through "blown-up" 3-cycles. This kind of duality has allowed to get the non-perturbative effective superpotential of N=1 gauge theories, like the Veneziano-Yankielowicz or Affleck-Dine-Seiberg superpotentials. Our future task will be to explore the relations between gauge/gravity correspondence and geometrical transitions in supersymmetric and non-supersymmetric string models, within the supersymmetric (with N=1 matter) and non-supersymmetric (orientifold field theories) previously considered. Starting from gravity or supergravity "deformed" geometries also caracterized by a non constant dilaton field, the aim of this activity is to determine non-perturbative effects of gauge theories, such as their corresponding superpotential. Finally, our research project foresees also to study gauge theories interesting from a phenomenological point of view that live on the world-volume of intersecting branes. In particular, our attention will be focused on perturbative and non-perturbative aspects of gauge theories by using the techniques of the open/closed string duality already developed in the case of parallel branes. Activity 3.2 - ADS/CFT correspondance W. Mueck The AdS/CFT correpondence is an important and modern tool to study aspects of gauge theories at coupling regimes that are not accessibly by ordinary perturbation theory. It is a holographic duality and builds on the fact that the dynamics of a given Supergravity theory on an (asymptotically) bulk anti-de Sitter space encodes the correlation functions of a certain (deformed) conformal field theory, which is known as its dual theory. There exists a precise method, known as Holographic Renormalization, that extracts the information relevant for the correlators from the bulk dynamics. A systematic and efficient method of Holographic Renormalization using the Hamilton-Jacobi approach has been developed and provides the basis of the holographic calculation of correlation functions in conformal gauge theories. The study of correlation functions in the so-called Holographic Renormalization Group (RG) flows, which are the duals of conformal field theories deformed by operator insertions or non-zero vacuum expectation values, is of great interest, because the RG flows include realistic phenomena, such as confinement. The technically challenging study of fluctuations in the bulk background configurations of interest has led to important results for two-point functions. However, the difficulties caused a halt in the research and literature on the topic, and most three-point functions were considered out-of-reach for present-day calculational methods. A gauge-invariant formalism for the treatment of fluctuations in Holographic RG flow backgrounds was developed, which elegantly removes the difficulties encountered previously . By using this formalism they have been computed the 3-point functions in a generic holographic GR flux. As a relevant application it has been considered the Girardello- Petrini-Porrati-Zaffaroni flux for which gluball scattering amplitudes have been computed. Such amplitudes imply selection rules for glueball decays which are not yet explained in the framework of Quantum Field Theories. Program for 2005 As a future program our aim is to generalize the computation of correlators in field theory through their respective dual in cases which are not asymptotically anti-de Sitter. These are just more relevant and there are some already well-known, as the Klebanov-Strassler and Maldacenza-Nunez solutions. Now-a-day it is not known how the supergravity dynamics encodes the correlation functions of the dual theory in these cases but a general formulation of the gauge-invariant formalism is an important step because it is applicable directly to the analysis of the gravity fluctuations. Once solved the bulk dynamics, it remains to establish the precise correspondence between gauge operators and bulk fields. Activity 3.3 - Statistical mechanics A. Coniglio, A. Caiazzo, A. de Candia, F. di Liberto, A. Fierro, M. Nicodemi, F. Peruggi, P. Ruggiero, M. Pica Ciamarra, M. Tarzia, T. Abete Our main research lines concern the physics of complex, disordered and glassy systems; granular media; soft matter; systems of biological interest. Such research lines are supported by national and international grants (EU, PRIN, FIRB, Regione,Ministero Affari Esteri). Our group is part of the "Laboratorio di Modellistica del Centro Regionale di Competenza AMRA", where we are also responsible for a 198 processor cluster. Main international collaborations are with: ESPCI in Paris and CNRS in Rennes, on granular media; Imperial College London on off-equilibrium systems; CNRS Montpelier and ESPCI in Paris on soft-matter; Saclay on biological systems. New scientific activities. Our team is involved in the development of "Distretto Tecnologico sui Materiali Polimerici e Compositi Strutturali della Campania". We have started a new research line on the applications of Statistical Mechanics to biophysics and bioinformatics. Activity 3.4. - Glass transition A. Caiazzo, A. Coniglio,A.de Candia,F. di Liberto A. Fierro, M. Nicodemi, M. Tarzia Theoretical model for glass transition We developed a model with self-generated disorder and local frustration which reproduces many features of glassy systems, in particular a dynamical transition is found satisfying the predictions of the mode coupling theory for supercooled liquids. Attractive glass We also introduced a generalized p-spin glass like model that captures some of the main features of attractive glasses (recently found by Mode Coupling investigations of attractive colloids) such as a glass/glass transition line and dynamical singularity points characterized by a logarithmic time dependence of the relaxation. Program for 2005 We will investigate its features not predicted by the Mode Coupling scenario that could further describe the attractive glasses behavior, such as aging effects with new dynamical singularity points ruled by logarithmic laws or the presence of a glass spinodal line. Activity 3.5 - Granular media A. Coniglio, A. Fierro, M. Nicodemi, M. Pica Ciamarra,M. Tarzia We have investigated by means of computer simulations (monte-carlo and molecular dynamics simulations), and mean field analytical approximations, two relevant questions rised by granular materials. The understanding of flowing grains, and the possibility of describing granular materials in a statistical mechanics framework. We have compared analytically, in mean field, the predictions of two different statistical mechanics approaches proposed to describe binary granular mixtures subjected to some external driving (continuous shaking or tap dynamics). Focusing on the phenomenon of size segregation, we have found that the two approaches give different predictions of the crossovers from BNE to RBNE with respect to the shaking amplitude, which could be detected experimentally. Program for 2005 We plan to investigate flowing grains, and particularly the role of dynamical instabilities in granular flow; and systems subject to a tap dynamics. Here we want to test Edward's statistical mechanics approach to granular media. Particularly we want to demonstarte the existence of phase transitions in granular mixtures, predicted by our mean filed calculations, via computer simulations. Our future research project concerns the study of the nature of the size segregation in granular mixtures. Introducing a mean field theory in the framework of a statistical mechanics approach for athermal systems, and by means of numerical simulations, we will study a new purely thermodynamic mechanism which gives rise to the size segregation phenomenon, which might be induced by a true phase transition.
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