• String Theory
• Vacuum Stability
• Supersymmetry Breaking
• Supergravity

In this Thesis we address the issue of perturbative stability of non–supersymmetric string vacua with AdS × S spacetime backgrounds. To this end, we build a framework which generalizes the Breitenlohner–Freedman criterion for perturbative vacuum stability in Field Theory and rests on the diagonalization of certain asymptotic mixing matrices of field fluctuations. After an introductory overview, which we present in Chapter 2 and is meant to highlight some current frontiers of String Theory, in Chapter 3 we review the key features of perturbative closed–string spectra and of their orientifold descendants in ten dimensions. We also explain how Supersymmetry breaking brings along, in the low–energy field theory, runaway potentials that destabilize an initial Minkowski vacuum. In Chapter 4 we then consider a class of AdS × S vacua that recently emerged, where the effect of tadpoles is compensated by suitable fluxes in AdS and/or in the internal spheres. In Chapter 5 we introduce the Breitenlohner–Freedman bound, computing it for various types of free fields in AdS, and in Chapter 6 we discuss the simplified asymptotic analysis of mixed systems of fluctuations. We then apply this method to the string vacua described in Chapter 4, diagonalizing the resulting asymptotic mass and mixing matrices, in order to compare the corresponding eigenvalues to the bounds. The resulting conditions for vacuum stability in different regimes of string couplings are then explored, and we identify two perturbatively stable vacua: an AdS3 × S7 orientifold vacuum and an AdS7 × S3 heterotic vacuum. Chapter 7 contains some concluding remarks.