Topological constraints in the LARGE-volume scenario

Abstract

We elaborate on recent results regarding the self-consistency of de Sitter vacua in the LARGE-volume scenario of type IIB string theory. In particular, we analyze to what extent the control over warping, curvature and gs corrections depends on the topology and the orientifold/brane data of a compactification. We compute a general bound on the magnitude of these corrections which strongly constrains the D3 tadpole. The minimally required tadpole ranges from $$ \mathcal{O} $$ O (500) to $$ \mathcal{O} $$ O (106) or more and depends strongly on other data, in particular on the Euler number of the Calabi-Yau 3-fold, the triple-self-intersection and Euler numbers of the small divisor and the coefficient as appearing in the non-perturbative superpotential. We give arguments suggesting that satisfying these constraints is very challenging and perhaps impossible.

Curvature corrections to KPV: Do we need deep throats?

“…It may even change sign, leading to non-SUSY AdS. This is in fact the situation which a pure anti-D3-analysis (without transition to the NS5) suggests [9]. Now, if one can tune the uplifting potential to extremely small values, one may be able to produce an exponentially suppressed uplift without relying on a deep warped throat.…”

“…[5,6]). In particular, a series of recent papers [7][8][9] has scrutinized the conditions required to achieve a de Sitter vacuum in the LVS using an anti-D3-brane uplift.…”

“…An effect which was not considered in [8] but was crucial to [7,9] derives from the α 2 curvature corrections to the action of the anti-D3-brane responsible for the uplift. They lead to the anti-D3-induced potential 1…”

“…where a, b are normal indices and α, β are tangent indices relative to the brane. References [7,9] demanded that the anti-D3-curvature corrections should be small compared compared to the leading order DBI action. In our opinion, it is not necessary to impose such a strong constraint, as we now explain: Note first that the curvature correction appears in the 4D scalar potential as a term which has the same dependence on the Kahler moduli as the tree-level tension.…”

“…Corrections like those in (1.1) are then dangerous and one should demand that they remain sufficiently small. However, it is sufficient to require that the corrections are small enough for the antibrane tension to remain positive, it is not necessary to demand that they are parametrically small as done in [7,9]. Moreover, in this case an alternate uplifting mechanism emerges which does not rely on the deep warped throat but instead tunes the anti-brane potential to be exponentially small because of curvature corrections.…”