Abstract
We consider dimensional reductions of M-theory on \U0001d54b7/ {mathrm{mathbb{Z}}}_2^3 with the inclusion of arbitrary metric flux and spacetime filling KK monopoles. With these ingredients at hand, we are able to construct a novel family of non-supersymmetric yet tachyon free Minkowski extrema. These solutions are supported by pure geometry with no extra need for gauge fluxes and possess a fully stable perturbative mass spectrum, up to a single flat direction. Such a direction corresponds to the overall internal volume, with respect to which the scalar potential exhibits a no-scale behavior. We then provide a mechanism that lifts the flat direction to give it a positive squared mass while turning Mkw4 into dS4. The construction makes use of the combined effect of G7 flux and higher curvature corrections. Our solution is scale separated and the quantum corrections are small. Finally we speculate on novel possibilities when it comes to scale hierarchies within a given construction of this type, and possible issues with the choice of quantum vacuum.
Highlights
On the other hand, stringy de Sitter constructions in general have recently been subject to some skepticism at a much more fundamental level
We consider dimensional reductions of M-theory on T7/Z32 with the inclusion of arbitrary metric flux and spacetime filling KK monopoles. With these ingredients at hand, we are able to construct a novel family of non-supersymmetric yet tachyon free Minkowski extrema. These solutions are supported by pure geometry with no extra need for gauge fluxes and possess a fully stable perturbative mass spectrum, up to a single flat direction
Inspired by the unitarity and entropy puzzles raised by dS geometry when written in its static patch, one may start wondering whether a healthy theory of quantum gravity should even allow for dS vacua in the first place
Summary
M-theory compactifications on twisted toroidal orbifolds have been widely studied in the last few decades [41, 42]. The starting point is to observe [45] that the search for critical points of the scalar potential arising from (2.3) can be restricted to the origin of the scalar manifold, i.e. where S = T = U = i, without loss of generality This comes at the price of keeping the flux parameters in table 1 completely arbitrary, since any non-compact SL(2, R) transformation needed to move any point to the origin would just reparametrize the superpotential couplings in (2.3). The above system of algebraic equations is homogenous, and one can always use an overall rescaling to fix e.g. d0 = 1 After such a procedure, there turn out to exist four independent one dimensional branches of solutions, two of which are supersymmetric and identical, while the other two are non-supersymmetric and still tachyon free for appropriate choices of points. Axionic directions: dilatonic directions: isotropic 1.025 171 0.158 575 0.001 076 0.500 241 0.001 362 0 non-isotropic 0.122 146 (×2) 0.000 673 (×2)
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