Bounds on tower mass scales in the presence of throats of different warping

TL;DR

This paper derives bounds on the tower mass scales in string compactifications with multiple warped throats, considering the effects of different warping strengths and their implications for the uplift potential and metastable de Sitter vacua.

Contribution

It provides a detailed analysis of bounds on tower mass scales in warped throat scenarios, accounting for multiple throats with varying warping, which was not thoroughly explored before.

Findings

The upper bound on the tower mass scale is set by the lowest tower mass or gravitino mass.

Stronger warping in a throat lowers the associated KK mass scale.

Bounds differ depending on whether the throat with uplift is strongly or weakly warped.

Abstract

In Type IIB flux compactification realizing the metastable de Sitter (dS) vacuum, the uplift potential can be generated by $\overline{\rm D3}$-branes at the tip of Klebanov-Strassler throat. Then the uplift potential obeys the scaling law with respect to the tower mass scale $m_{\rm sc}$, which can be the Kaluza-Klein (KK) mass scale associated with the throat containing $\overline{\rm D3}$-branes or the bulk tower mass scales, depending on the warping of the throat. On the other hand, in the presence of another throat of stronger warping, the KK mass scale associated with this throat is lower than $m_{\rm sc}$. Nevertheless, the Higuchi bound and the condition that the tower mass scale is higher than the gravitino mass provide the upper bound on $m_{\rm sc}$ determined by the lowest tower mass scale (or gravitino mass). This bound also can be interpreted as the lower bound on the lowest tower mass scale determined by $m_{\rm sc}$. We investigate this bound in detail when the throat containing $\overline{\rm D3}$-branes is strongly and weakly warped, respectively.