Curvatures and potential of M–theory inD= 4 with fluxes and twist

Abstract

We give the curvatures of the free differential algebra (FDA) of M-theory compactified to D = 4 on a twisted seven-torus with the 4-form flux switched on. Two formulations are given, depending on whether the 1-form field strengths of the scalar fields (originating from the 3-form gauge field (3) ) are included or not in the FDA. We also give the bosonic equations of motion and discuss at length the scalar potential which emerges in this type of compactifications. For flat groups we show the equivalence of this potential with a dual formulation of the theory which has the full E 7(7) symmetry.

On the moduli space of spontaneously broken N = 8 supergravity

“…In fact, the first two models already appear in Table 3 and have N = 4 and N = 2 supersymmetry respectively. Moreover, we can see that 47) hence also this model already appeared in Table 3. As shown in [29], [23], these models have 3 de Sitter vacua in the range c ∈ [0, √ 2 − 1[, one already known for c = 0 and two genuinely new.…”

“…This allows to reproduce the most general CSS gauging with up to four non-zero mass parameters m i . It is known how to reproduce a similar result from M -theory reductions on twisted tori [30,[46][47][48][49], but it is also known that such geometric reductions can only produce at most 3 of the 4 mass parameters of the CSS models. By a simple comparison of the potential terms of N = 8 supergravity with those generated by flux compactifications of M -theory, assuming a framework where the starting point defining the electric frame of the 4-dimensional theory is the compactification on a torus, we can identify the fourth mass parameter with a non-geometric flux: θ 77 .…”

“…In [56], [30], [46], [47], [49] it has been established that the CSS gaugings with up to 3 independent mass parameters can arise from reductions of M-theory on a twisted 7-dimensional 7 , following the construction in [48] where c can be either 0 (singular variety) or 1/2 (smooth manifold) and in the following we take c = 0, for simplicity.…”

Supersymmetric completion of M-theory 4D-gauge algebra from twisted tori and fluxes

“…The supercovariant field strengths originate by projecting these components on the dx µ basis. The 7-form flux [42], which we shall denote byg M N P QRST =gǫ M N P QRST , transforms in the 1 +7 of GL(7, R) enters our discussion as an intregration constant which comes about when integrating the eleven dimensional field equation [33]:…”

Lectures on gauged supergravity and flux compactifications

“…We have thus identified the relevant flux parameters within the 912 components of the general embedding tensor and derived the full set of quadratic consistency relations among them. To complete the analysis it remains to evaluate the full Lagrangian of [42] and in particular the scalar potential (3.45) for these particular embedding tensors, which we will not do here, see [81,82] for some results. In principle, the very same analysis can be continued for those gaugings induced by the lower lying entries of (4.19).…”