Five-dimensional aspects of M-theory dynamics and supersymmetry breaking

Abstract

We discuss the reduction of the eleven-dimensional M-theory effective Lagrangian, considering first compactification from eleven to five dimensions on a Calabi-Yau manifold, followed by reduction to four dimensions on an S 1 /Z 2 line segment at a larger distance scale. The CalabiYau geometry leads to a structure of the five-dimensional Lagrangian that has more freedom than the eleven-dimensional theory. In five dimensions one obtains a non-linear σ model coupled to gravity, which implies non-trivial dynamics for the scalar moduli fields in the bulk of the Z 2 orbifold. We discuss solutions to the five-dimensional equations of motion in the presence of sources localized on the boundaries of the Z 2 orbifold that may trigger supersymmetry breaking, e.g., gaugino condensates. The transmission of supersymmetry breaking from the hidden wall to the visible wall is demonstrated in specific models. The rôle of the messenger of supersymmetry breaking may be played by the gravity supermultiplet and/or by scalar hypermultiplets. The latter include the universal hypermultiplet associated with the Calabi-Yau volume, and also the hypermultiplets associated with deformations of its complex structure, which mix in general.

Options for gauge groups in five-dimensional supergravity

“…Two cases should be distinguished (see also [6,13,22]). 5 As mentioned earlier, and contrary to what happens in four dimensions [21,22], this potential vanishes when no tensor fields are present. This can be seen directly from (2.14), taking into account the fact that the very special geomety of M V S implies [11] that K x I hĨ = 0 when the summation goes over the full set of indicesĨ.…”

“…For example, this effective theory frequently plays an essential rôle in mediating supersymmetry breaking between the brane on which it originates and the brane where the Standard Model is localized [5].…”

Five-branes and supersymmetry breaking in M-Theory

“…Supersymmetry breaking in five dimensions was also studied in [48,33,45]. Furthermore, we will calculate the matter field part of the D = 4 low energy effective action in its generic form.…”

Supersymmetry Breaking in M-theory

“…However, if Λ > m 5 , in order to understand the pattern of supersymmetry breaking, one needs the full four-dimensional Lagrangian constructed by the compactification chain d = 11 → 5 → 4 [6,7,8,9,10,11]. For this, one must first study how the low-energy four-dimensional model arises out of the two d = 10 → 4 sectors which are spatially disconnected in the original d = 11 → 5 theory, in other words, how the two gauge sectors are combined together in course of the compactification process.…”

“…The question of supersymmetry transmission through the bulk in the five-dimensional supergravity was discussed in previous papers [9], [10], [7], [12], [13], [14], [15], [16]. The reader should be warned that different approaches seem to give somewhat different results.…”