Weakly coupled de Sitter vacua with fluxes and the swampland

131

158

We propose an alternative refined de Sitter conjecture. It is given by a natural condition on a combination of the first and second derivatives of the scalar potential. We derive our conjecture in the same weak coupling, semi‐classical regime where the previous refined de Sitter conjecture was derived, using the same tools together with a few more assumptions that we discuss. We further test and constrain free parameters in our conjecture using data points of a classical type IIA supergravity setup. Interestingly, our conjecture easily accommodates slow‐roll single field inflation with a concave potential, favored by observations. The standard quintessence potential is in tension with our new conjecture, and we thus propose a different type of quintessence model.

g_{s}

, and a small number of O 6 .…”

Section: Testing the New Conjecturesupporting

confidence: 77%

Further Refining the de Sitter Swampland Conjecture

Andriot

Roupec

2019

131

158

“…Nevertheless, the tools developed allowed us to obtain further existence constraints in , and another suggestion for the tachyon. Conjecture : we first showed, for

p = 4, 5, 6

, that this conjecture would hold unless the compact manifold admits a hierarchy such that

false| {scriptR}_{6} false| \times L^{2} ≪ 1

, where L is an average internal length . We were not able to exclude the possibility of such an internal hierarchy in a classical de Sitter solution, despite interesting arguments of [], and detailed information from the Einstein equation seemed needed to that end. Interestingly, we showed that having this hierarchy would lead to a scale separation with 4d.…”

Section: Results Summarymentioning

confidence: 95%

“…This idea was recently put forward in [] when analysing known classical de Sitter solutions of type IIA supergravity: those appeared inconsistent with a stringy origin, because of these extra requirements. This question was then studied formally and exemplified for

p = 6

in []: the conclusions turned out consistent with conjecture , without being fully general. We investigate this question here for

p = 4, 5, 6

in a 10d approach and argue that one cannot conclude on a proof of conjecture with the tools developed so far.…”

Section: Conjecture 3: No Supergravity Solution With String Originmentioning

confidence: 91%

“…We combine appropriately the Equations , , , to be satisfied by de Sitter solutions. We read from , using that

F_{6 - p} \neq 0

3 g_{s} \frac{T_{10}}{p + 1} > - 2 {scriptR}_{6} \Rightarrow N_{s} > \frac{2}{3} \frac{N_{f}^{2}}{g_{s}} {((), \frac{L}{l_{s}})}^{7 - p} .

It is tempting to conclude from a proof of conjecture : indeed, taking

N_{f}^{2} \geq 1

, the requirements

L ≫ l_{s}

and

g_{s} ≪ 1

lead to a large right‐hand side since

p = 4, 5, 6

, forcing

N_{s}

to be larger than its bound; this point was made already for

p = 6

in []. For instance, a hierarchy of order 10 gives already

N_{s}

of at least 100, which is above the standard value of

2^{9 - p}

.…”

Section: Conjecture 3: No Supergravity Solution With String Originmentioning

confidence: 99%

“…This would exclude the possibility of our internal hierarchy. Several possible loopholes were however mentioned in []. The most relevant one to us is the fact that, even on a group manifold,

R_{6}

could be a complicated function of the various fields, without a fixed sign, and its dependence on the appropriate α is hard to predict in our view.…”

Section: Conjecture 3: No Supergravity Solution With String Originmentioning

confidence: 99%

See 2 more Smart Citations

Open Problems on Classical de Sitter Solutions

Andriot

2019

122

Classical 10d string backgrounds with a 4d de Sitter space‐time, D‐brane and orientifold sources, are commonly believed to satisfy the following: 1.There is no classical de Sitter solution with parallel sources. 2.Classical de Sitter solutions with intersecting sources are unstable. 3.Classical de Sitter solutions cannot have at the same time a large internal volume, a small string coupling, a bounded number of orientifolds and quantized fluxes. These three conjectures are of particular relevance to the swampland program, and if true, they challenge the connection of string theory to cosmology. We restrict here to a standard solution ansatz for which the problem is well‐defined, and we still fail to prove analytically any of these conjectures. While developing new tools and obtaining new constraints, we identify remaining corners of parameter space where counter‐examples to these conjectures could be found.

The Swampland: Introduction and Review

Palti

2019

898

1,097

The Swampland program aims to distinguish effective theories which can be completed into quantum gravity in the ultraviolet from those which cannot. This article forms an introduction to the field, assuming only a knowledge of quantum field theory and general relativity. It also forms a comprehensive review, covering the range of ideas that are part of the field, from the Weak Gravity Conjecture, through compactifications of String Theory, to the de Sitter conjecture.