Aspects of compactification on a linear dilaton background
Résumé
We consider the most general Kaluza-Klein (KK) compactification on S$^{1}$/ℤ$_{2}$ of a five dimensional (5D) graviton-dilaton system, with a non-vanishing dilaton background varying linearly along the fifth dimension. We show that this background produces a Higgs mechanism for the KK vector coming from the 5D metric, which becomes massive by absorbing the string frame radion. The $ \mathcal{N} $ = 2 minimal supersymmetric extension of this model, recently built as the holographic dual of Little String Theory, is then reinvestigated. An analogous mechanism can be considered for the 4D vector coming from the (universal) 5D Kalb-Ramond two-form. Packaging the two massive vectors into a spin-3/2 massive multiplet, it is shown that the massless spectrum arranges into a $ \mathcal{N} $ = 1, D = 4 supersymmetric theory. This projection is compatible with an orbifold which preserves half of the original supersymmetries already preserved by the background. The description of the partial breaking $ \mathcal{N} $ = 2 → $ \mathcal{N} $ = 1 in this framework, with only vector multiplets and no hypermultiplets, remains an interesting open question which deserves further investigation.