Abstract
We consider the most general Kaluza-Klein (KK) compactification on S1/ℤ2 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.
Highlights
Closed string amplitudes being proportional to gS, in this limit the branes and bulk dynamics decouple
We conclude that the original N = 1 supersymmetry preserved by the linear dilaton background on R1,4 remains preserved after the compactification of the fifth direction on S1/Z2, provided the branes added at the two boundaries of the interval are NS5-branes
The work carried out in this paper analysed different aspects of the linear dilaton background arising from a runaway scalar potential in five dimensions, in relation to two different perspectives: compactification and supersymmetry breaking
Summary
Where gMN is the five-dimensional metric in the string frame (not to be confused with the Einstein frame metric GMN which will be introduced below), φ the dilaton field, and Λ a constant introducing a runaway dilaton potential, characteristic of non-critical string theory. Varying S with respect to φ and gMN yields the equation of motion of the dilaton and the five-dimensional Einstein equations, respectively given by:. One can check that these equations are solved by the five-dimensional Minkowski metric, in addition of a linearly varying dilaton along the fifth direction y, breaking the 5D Poincaré invariance into a 4D one, gMN = ηMN , φ = αy,. Eq (2.18) shows that consistency of the equations of motion requires a system of branes of opposite tensions to set at the fixed points y = 0 and y = L of the S1/Z2 orbifold, to the Randall-Sundrum model.. The solution at the boundaries arising from the classical equations of motion consists of NS5-branes, as expected from the LST string theory approach.
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