Classical de Sitter solutions in three dimensions without tachyons?

Abstract

We continue the study of compactifications of massive IIA supergravity on G2 orientifolds and demonstrate that breaking supersymmetry with anti-D2 and anti-D6 sources leads to 3d theories for which the typical tachyons haunting classical dS solutions can be absent. However for a concrete torus example the meta-stable dS window disappears after a quantization of fluxes and charges. We discuss the prospects of more general G2 compactifications and argue that they could potentially alleviate the tachyon problem by introducing larger tadpole numbers and warped throats. However, exactly those ingredients then seem to push the vacuum towards the brink of perturbative brane–flux decay in the open string sector. This is either a remarkable illustration of the no-dS swampland conjecture or such vacua live in very difficult to control regions of parameter space.

Three-dimensional flux vacua from IIB on co-calibrated G2 orientifolds

“…For the reasons outlined above, in this work we continue the study of Type II string flux compactifications with threedimensional external space and minimal supersymmetry, that was initiated in [14,15]. As shown in those works, Type II on G2 holonomy manifolds has offered the possibility to scrutinize the swampland conjectures.…”

“…3 From (5.7) we also see why one cannot get de Sitter vacua from Type I by simply adding anti-D5s, and instead we have to switch to the BSB setup to be able to even discuss such possibility. The fact that one may need two types of supersymmetry breaking sources to get classically stable de Sitter vacua was already alluded to in [15] and as we will see we will need here both anti-D5s and anti-D9s as well, once we discuss the shape moduli stabilization.…”

“…It is important to point out that the non-vanishing covariant derivative ∇ = 0 signifies a deviation from G2 holonomy and implies a non-vanishing Ricci tensor which is a key feature of this work. Previous works [14,15] studied the case where ∇ = 0 and thus all torsions were simultaneously set to zero, the internal space was Ricci flat and the G2 structure group was equivalent to the G2 holonomy of the manifold. Here instead the form of the Ricci scalar is R (7)…”

“…Actually, achieving full moduli stabilization including thes a is challenging, and we do not have a systematic way of tackling this question. However it is instructive to see first if we can generate the de Sitter vacua with the co-calibrated G2 geometry we have at hand following the methodology we also followed in [15]. This does not give the most general de Sitter solution but it offers a simple way to obtain it.…”

“…As a result the properties of such vacua can be cross-checked with 2D CFT methods. Secondly, from a technical point of view, the field content of a 3D flux compactification is considerably simpler than the 4D counter-parts which allows to perform a more thorough study of such vacua [14,15]. For example, the minimal supersymmetric background in 3D allows half of the number of supersymmetries than the minimal 4D background.…”