Tachyons in Classical de Sitter Vacua

TL;DR

This work analyzes classical de Sitter vacua in the two-derivative supergravity limit of type II string theory, focusing on tachyonic instabilities that plague known constructions. By examining two explicit models—the $SU(3)$-structure orientifold in massive IIA with O6-planes and the $SU(2)$-structure orientifold in IIB with O5/O7-planes—the authors identify tachyons as arising from strong metric deformations that bring solutions near a SUSY Minkowski point and from large mixing between the sgoldstino and orthogonal moduli. A generalized sgoldstino no-go shows that tachyons lie close to, but not exactly along, the sgoldstino direction due to off-diagonal mass matrix terms, a picture supported by analytic IIA results and a corroborating IIB example. The findings illuminate a structural origin of instability in classical dS vacua, offer a practical stability criterion based on $m_{\phi}^2$ and $V_{\phi j}$, and suggest avenues (e.g., non-geometric fluxes or extra ingredients) to pursue metastable solutions in the string landscape.

Abstract

We revisit the possibility of de Sitter vacua and slow-roll inflation in type II string theory at the level of the classical two-derivative supergravity approximation. Previous attempts at explicit constructions were plagued by ubiquitous tachyons with a large $η$ parameter whose origin has not been fully understood so far. In this paper, we determine and explain the tachyons in two setups that are known to admit unstable dS critical points: an SU(3) structure compactification of massive type IIA with O6-planes and an SU(2) structure compactification of type IIB with O5/O7-planes. We explicitly show that the tachyons are always close to, but never fully aligned with the sgoldstino direction in the considered examples and argue that this behavior is explained by a generalized version of a no-go theorem by Covi et al, which holds in the presence of large mixing in the mass matrix between the sgoldstino and the orthogonal moduli. This observation may also provide a useful stability criterion for general dS vacua in supergravity and string theory.

Figures (1)

• Figure 1: A plot of the $m_{\alpha}^2=0$ surface (yellow) and the sgoldstino (red) using the first few orders of the $\epsilon$-expansion. Directions which lie inside of the surface have negative principal minors and are therefore sufficient to prove the existence of a tachyon by Sylvester's criterion. For $\epsilon\to 0$, the surface shrinks to a point and aligns with the sgoldstino.