Proprietà dei vuoti eterotici non-supersimmetrici

In my Master Thesis I am interested in the study of non-supersymmetric string constructions, where supersymmetry is spontaneously broken via compactification. In particular, I am interested in deciphering the information encoded in the vacuum energy. Strings describe infinitely many modes, and their vacuum amplitudes satisfy a number of geometric constraints, that in a wide class of models essentially determine the full perturbative spectrum. At one loop a closed oriented string sweeps a torus, and one is instructed to integrate over all inequivalent tori. This amounts to restricting the integration over a fundamental domain and requires that the integrand function is an automorphic function of PSL(2,Z), the latter condition being equivalent to impose suitable GSO projections on the full string spectrum. Although the GSO truncation selects consistent string vacua and constrains the distribution of physical and unphysical states at each mass level, it is actually cumbersome to extract information about the graded number of degrees of freedom at arbitrary mass. However, the mass distribution of bosonic and fermionic excitations plays a crucial role in determining the celebrated finiteness of string theory. Although space-time supersymmetry on flat space imposes a perfect equilibrium between bosonic and fermionic degrees of freedom, this is no longer evident when supersymmetry is absent or spontaneously broken. Most of presently known string vacua are classically unstable when space-time supersymmetry is absent. String spectra are typically plagued by the presence of tachyonic modes that suggest the onset of an instability. If one insists that a non-supersymmetric vacuum ought to be predictive, at least classically, one is bound to consider only string configurations where tachyonic excitations are absent. A first attempt to study the interplay between massive states and tachyons has shown that infra-red finiteness of the one-loop vacuum energy of closed oriented strings actually requires the presence of space-time fermions in the spectrum, and moreover their overall number, independently of the mass, must cancel against the space-time bosons almost exactly. Because of this exact cancellation between bosonic and fermionic degrees of freedom, this property of the stable spectrum was termed asymptotic supersymmetry and put a first constraint on the overall distribution of degrees of freedom of classically stable string configurations. In subsequent works, this (global) asymptotic supersymmetry of classically stable string vacua was promoted to a (local) misaligned supersymmetry whereby a surplus of bosonic/fermionic excitations alternate in the tower or string states. Understanding what happens to the string spectrum at the onset of tachyonic instabilities is the main subject of my studies. In particular, I shall focus on string models where supersymmetry is broken by the Scherk-Schwarz mechanics. Since the latter is a continuous deformation of the string spectrum, where supersymmetry is recovered in the decompactification limit, asymptotic supersymmetry is expected to be present at any point in the classical moduli space, also in regions where string states with non-trivial winding numbers can become tachyonic. Less obvious is the fate of misaligned supersymmetry.