Science/Research

   Current research:
   

2012-present (CSIC, Madrid)
Research develops in multiple directions, from open issues in 2d CFTs and Gepner models to 4d Supersymmetry and superconformal field theories.
In particular, in this paper we consider the light-cone embedding of the superconformal group in four dimensions in the case of extended supersymmetry, hence generalizing an earlier work of Goldberger, Skiba and Son which was restricted at N=1. Moreover, we work out explicitly the case of N=2 chiral superfields in four dimensions, putting the component fields in correspondence with Pascal's pyramid at layer N. This correspondence is a generic property of the N-extended chiral sector.

   Past research:
   

2009-2011 (Nikhef, Amsterdam)
In the context of string theory phenomenology, we apply previously determined results in 2d CFT's to Gepner models.
It is well-known that in order to have N=1 spacetime supersymmetry, N=2 supersymmetry is needed on the string worldsheet. Representation of the N=2 super conformal algebra are infinite dimensional if the central charge is larger than 3, but finite dimensional if it is smaller. These finite-dimensional representation, known as N=2 minimal models, are classified in terms of their weights, charges and sectors, up to field identifications which reduce the number of independent primaries.
Gepner models are constructed as tensor product of minimal models, with the only restriction that, for four-dimensional string compactifications, the total internal central charge adds up to 9. Moreover, additional constraints are needed to ensure supersymmetry. These constraints are easily implemented by simple-current extensions.
Suppose now that in a Gepner model (at least) two of the factors in the tensor product are equal. There exists then a manifest symmetry which exchanges these two factors. Hence one can mod out the flipping symmetry to obtain a completely new theory. The resulting theory is nothing else but the permutation orbifold, of which many new interesting outcomes have been obtained recently, especially in connection with simple-current extensions.

2007-2009
In the attempt of making contact with phenomenology and addressing open issues with branes, we develop new tools in two-dimensional conformal field theory that we would like to apply in string theory compactifications. In particular, we start from integer spin simple current extensions of a conformal model. If the currents leave some fields fixed, hereafter referred to as fixed points, the S matrix of the extended theory cannot be trivially derived. This can happen when the current has integer or half-integer spin. It will be instead parameterized by a set of theory-dependent ``S^J'' matrices. These matrices are already known for WZW models and coset models.
We consider orbifold conformal field theories, where the mother theory is tensored with itself and the whole product is modded out by the resulting exchanging symmetry of the two factors, and extend it by all its possible integer spin simple currents. Moreover, fixed points arise in the permutation orbifold. We determine the S^J matrices of these models, first considering a few specific instances (e.g. the B(n)₁ and D(n)₁ series for all value of n; the SU(2)_k model, fully when k=2 or odd, partially when k is even) and then giving a general ansatz which depends only on the S and T matrices of the original theory. This ansatz satisfies unitarity, modular invariance and in addition produces integer fusion coefficients.

2005-2007 (University of Amsterdam)
After a quite extensive study of Conformal Field Theory and the understanding of several aspects of String Theory (in the Green-Schwarz and the RNS formulations) and of its most important components (like supersymmetry - both on the world sheet and the spacetime -, branes, gauge fields, BPS states), we have turned to some open problems (like the conjecture of M Theory as a matrix theory and the AdS/CFT correspondence).
Our work is related both to mathematical and physical aspects. From the mathematical side, we have faced the subject of (compact) Riemann surfaces of arbitrary genus (harmonic and holomorphic differentials, divisors, Riemann-Roch theorem, theta functions, holomorphic line bundles). From the physical side, we have focused on dyon counting problems and CHL models. Moreover, we have deeply looked at the black hole entropy (function), together with the related topics of attractors and special geometry.

2004-2005 (University of Bologna)
Starting from the observation that the Hawking radiation, which can be derived in the context of Quantum Field Theory in curved spacetimes, is very unlikely to be detected, we have developed some more understanding about analogue models of black holes, and in particular about acoustic models.
After explaining in which situations acoustic black holes can occur and the reasons why we can expect a corresponding Hawking radiation from the acoustic horizon, using the formalism and the technology of Quantum Field Theory in curved spacetimes, we put forward the question about the backreaction, i.e. we analyze how the emitted radiation influences the evolution of the acoustic black hole.
The backreaction equations have been derived in four dimensions and solved perturbatively in two dimensions, after dimensional reduction. The result is that the horizon shrinks and the temperature of the radiation decreases in time: the same behavior is expected for charged Reissner-Nordstrom gravitational black holes.