A 4D IIB flux vacuum and supersymmetry breaking. Part I : Fermionic spectrum

We consider the type-IIB supergravity vacua that include an internal T5, depend on a single coordinate r and respect a four-dimensional Poincaré symmetry, with the aim of highlighting low-energy spectra with broken supersymmetry and a bounded string coupling. These vacua are characterized by the flux Φ of the self-dual five form in the internal torus, the length ℓ of the interval described by the coordinate r, a dilaton profile that is inevitably constant and a strictly positive dimensionless parameter h. As ℓ → ∞ while retaining finite values for Φ and ℓh−54, half of the original ten-dimensional supersymmetry is recovered, while finite values of ℓ break it completely. In the large-ℓ limit one boundary disappears but the other is still present, and is felt as a BPS orientifold by a probe brane. In this paper we focus on the fermionic zero modes and show that, although supersymmetry is broken for finite values of ℓ, they are surprisingly those of four-dimensional N = 4 supergravity coupled to five vector multiplets. Still, the gravitini can acquire masses via radiative corrections, absorbing four of the massless spin-12 modes.