Antonella Liccardo

Classical gauge instantons from open strings

We study the D3/D(-1) brane system and show how to compute instanton corrections to correlation functions of gauge theories in four dimensions using open string techniques. In particular we show that the disks with mixed boundary conditions that are typical of the D3/D(-1) system are the sources for the classical instanton solution. This can then be recovered from simple calculations of open string scattering amplitudes in the presence of D-instantons. Exploiting this fact we also relate this stringy description to the standard instanton calculus of field theory.

D Branes in String Theory, I

In these lectures we present a detailed description of the origin and of the construction of the boundary state that is now widely used for studying the properties of D branes.

(F,Dp) bound states from the boundary state ∗

Abstract We use the boundary state formalism to provide the full conformal description of (F,D p ) bound states. These are BPS configurations that arise from a superposition of a fundamental string and a D p -brane, and are charged under both the NS–NS antisymmetric tensor and the ( p +1)-form R–R potential. We construct the boundary state for these bound states by switching on a constant electric field on the world-volume of a D p -brane and fix its value by imposing the Dirac quantization condition on the charges. Using the operator formalism we also derive the Dirac–Born–Infeld action and the classical supergravity solutions corresponding to these configurations.

On the gauge/gravity correspondence and the open/closed string duality

In this paper we review the conditions for the validity of the gauge/gravity correspondence in both supersymmetric and nonsupersymmetric string models. We start by reminding what happens in type IIB theory on the orbifolds ℂ2/ℤ2 and ℂ3/(ℤ2 x ℤ2), where this correspondence beautifully works. In these cases, by performing a complete stringy calculation of the interaction among D3-branes, it has been shown that the fact that this correspondence works is a consequence of the open/closed duality and of the absence of threshold corrections. Then we review the construction of type 0 theories with their orbifolds and orientifolds having spectra free from both open and closed string tachyons and for such models we study the validity of the gauge/gravity correspondence, concluding that this is not a peculiarity of supersymmetric theories, but it may work also for nonsupersymmetric models. Also in these cases, when it works, it is again a consequence of the open/closed string duality and of vanishing threshold corrections.

Gauge/gravity correspondence from open/closed string duality

We compute the annulus diagram corresponding to the interaction of a fractional D3 brane with a gauge field on its world-volume and a stack of N fractional D3 branes on the orbifolds 2/2 and 3/(2 ? 2). We show that its logarithmic divergence can be equivalently understood as due either to massless open string states circulating in the loop or to massless closed string states exchanged between two boundary states. This follows from the fact that, under open/closed string duality, massless states in the open and closed string channels are matched into each other without mixing with massive states. This explains why the perturbative properties of many gauge theories living on the world-volume of less supersymmetric and nonconformal branes have been recently obtained from their corresponding supergravity solution.

Kahler Metrics and Yukawa Couplings in Magnetized Brane Models

Using the field theoretical approach introduced by Cremades, Ibanez and Marchesano for describing open strings attached to D9 branes having different magnetizations, we give a procedure for determining the Kahler metrics of those open strings in toroidal compactifications.

Wrapped magnetized branes: two alternative descriptions?

We discuss two inequivalent ways for describing magnetized D-branes wrapped N times on a torus T2. The first one is based on a non-abelian gauge bundle U(N), while the second one is obtained by means of a Narain T-duality transformation acting on a theory with non-magnetized branes. We construct in both descriptions the boundary state and the open string vertices and show that they give rise to different string amplitudes. In particular, the description based on the gauge bundle has open string vertex operators with momentum dependent Chan-Paton factors.

Consistent off-shell tree string amplitudes

We construct off-shell tree bosonic string amplitudes, based on the operatorial formalism of the N-string vertex, with three external massless states both for open and closed strings by requiring them to be projective invariant. In particular our prescription leads, in the low-energy limit, to the three-gluon amplitude in the usual covariant gauge.

Gauge theories from D-branes.

In these lectures we start with a pedagogical introduction of the properties of open and closed superstrings and then, using the open/closed string duality, we construct the boundary state that provides the description of the maximally supersymmetric Dp branes in terms of the perturbative string formalism. We then use it for deriving the corresponding supergravity solution and the Born-Infeld action and for studying the properties of the maximally supersymmetric gauge theories living on their worldvolume. In the last section of these lectures we extend these results to less supersymmetric and non-conformal gauge theories by considering fractional branes of orbifolds and wrapped branes.

A Lattice Model for Influenza Spreading

We construct a stochastic SIR model for influenza spreading on a D-dimensional lattice, which represents the dynamic contact network of individuals. An age distributed population is placed on the lattice and moves on it. The displacement from a site to a nearest neighbor empty site, allows individuals to change the number and identities of their contacts. The dynamics on the lattice is governed by an attractive interaction between individuals belonging to the same age-class. The parameters, which regulate the pattern dynamics, are fixed fitting the data on the age-dependent daily contact numbers, furnished by the Polymod survey. A simple SIR transmission model with a nearest neighbors interaction and some very basic adaptive mobility restrictions complete the model. The model is validated against the age-distributed Italian epidemiological data for the influenza A(H1N1) during the season, with sensible predictions for the epidemiological parameters. For an appropriate topology of the lattice, we find that, whenever the accordance between the contact patterns of the model and the Polymod data is satisfactory, there is a good agreement between the numerical and the experimental epidemiological data. This result shows how rich is the information encoded in the average contact patterns of individuals, with respect to the analysis of the epidemic spreading of an infectious disease.