Tunneling approach and thermality in dispersive models of analogue gravity

We set up a tunneling approach to the analogue Hawking effect in the case of models of analogue gravity which are affected by dispersive effects. An effective Schroedinger-like equation for the basic scattering phenomenon IN->P+N*, where IN is the incident mode, P is the positive norm reflected mode, and N* is the negative norm one, signalling particle creation, is derived, aimed to an approximate description of the phenomenon. Horizons and barrier penetration play manifestly a key-role in giving rise to pair-creation. The non-dispersive limit is also correctly recovered. Drawbacks of the model are also pointed out and a possible solution ad hoc is suggested.

A new CY elliptic fibration and tadpole cancellation

Tadpole cancellation in Sen limits in F-theory was recently studied by Aluffi and Esole. We extend their results, generalizing the elliptic fibrations they used and obtaining a new case of universal tadpole cancellation, at least numerically. We could not find an actual Sen limit having the correct brane content, and we argue that such a limit may not exist. We also give a uniform description of the fibration used by Aluffi and Esole as well as a new, simple, fibration which has non-Kodaira type fibers.

Dielectric black holes induced by a refractive index perturbation and the Hawking effect

We consider a 4D model for photon production induced by a %superluminal refractive index perturbation in a dielectric medium. We show that, in this model, we can infer the presence of a Hawking type effect. This prediction shows up both in the analogue Hawking framework, which is implemented in the pulse frame and relies on the peculiar properties of the effective geometry in which quantum fields propagate, as well as in the laboratory frame, through standard quantum field theory calculations. Effects of optical dispersion are also taken into account, and are shown to provide a limited energy bandwidth for the emission of Hawking radiation.

Conserved quantities for the Sitter particles$^*$

Recent observations of the luminosity-red shift relation of distant type Ia supernovae established the fact that the expansion of the universe is accelerated. This is interpreted by saying that there exists some kind of agent (called dark energy), which exerts an overall repulsive effect on ordinary matter. Dark energy contributes today in the amount of about 73 % to the total energy content of the universe, and its spatial distribution is compatible with perfect uniformity. The simplest possible explanation for dark energy is to assume that it is just a universal constant, the so called cosmological constant. This would mean that the background arena for all natural phenomena, once all physical matter-energy has been ideally removed, is the de Sitter space time. Thus, the Poincare group should be replaced by the de Sitter group, and one is naturally led to a reformulation of the theory of special relativity on these grounds. The absence of a privileged class of equivalent frames (inertial frames) suggests that, in de Sitter relativity it would be desirable, to characterize significant physical quantities in an intrinsic way, namely in a manner independent of the choice of any particular coordinate patch. In this talk we would like to show how this can be accomplished for any set of independent conserved quantities along the geodesic motion of a free de Sitter particle. These quantities allow for a natural discussion of classical pointlike scattering and decay processes.

On a polynomial zeta function

We introduce a polynomial zeta function $zeta^{(p)}_{P_n}$, related to certain problems of mathematical physics, and compute its value and the value of its first derivative at the origin $s=0$, by means of a very simple technique. As an application, we compute the determinant of the Dirac operator on quaternionic vector spaces.

Genus four superstring measures

A main issue in superstring theory are the superstring measures. DHoker and Phong showed that for genus two these reduce to measures on the moduli space of curves which are determined by modular forms of weight eight and the bosonic measure. They also suggested a generalisation to higher genus. We showed that their approach works, with a minor modification, in genus three and we announced a positive result also in genus four. Here we give the modular form in genus four explicitly. Recently S. Grushevsky published this result as part of a more general approach.

Special Relativity in the 21$^{rm st}$ century

This paper, which is meant to be a tribute to Minkowskis geometrical insight, rests on the idea that the basic observed symmetries of spacetime homogeneity and of isotropy of space, which are displayed by the spacetime manifold in the limiting situation in which the effects of gravity can be neglected, leads to a formulation of special relativity based on the appearance of two universal constants: a limiting speed $c$ and a cosmological constant $Lambda$ which measures a residual curvature of the universe, which is not ascribable to the distribution of matter-energy. That these constants should exist is an outcome of the underlying symmetries and is confirmed by experiments and observations, which furnish their actual values. Specifically, it turns out on these foundations that the kinematical group of special relativity is the de Sitter group $dS(c,Lambda)=SO(1,4)$. On this basis, we develop at an elementary classical and, hopefully, sufficiently didactical level the main aspects of the theory of special relativity based on SO(1,4) (de Sitter relativity). As an application, we apply the formalism to an intrinsic formulation of point particle kinematics describing both inertial motion and particle collisions and decays.

Conservation laws and scattering for de Sitter classical particles

Starting from an intrinsic geometric characterization of de Sitter timelike and lightlike geodesics we give a new description of the conserved quantities associated with classical free particles on the de Sitter manifold. These quantities allow for a natural discussion of classical pointlike scattering and decay processes. We also provide an intrinsic definition of energy of a classical de Sitter particle and discuss its different expressions in various local coordinate systems and their relations with earlier definitions found in the literature.

Two loop superstring amplitudes and S_6 representations

In this paper we describe how representation theory of groups can be used to shorten the derivation of two loop partition functions in string theory, giving an intrinsic description of modular forms appearing in the results of DHoker and Phong [1]. Our method has the advantage of using only algebraic properties of modular functions and it can be extended to any genus g.