A new class of de Sitter vacua in String Theory Compactifications

Abstract

We revisit the stability of the complex structure moduli in the large volume regime of type-IIB flux compactifications. We argue that when the volume is not exponentially large, such as in Kähler uplifted dS vacua, the quantum corrections to the tree-level mass spectrum can induce tachyonic instabilities in this sector. We discuss a Random Matrix Theory model for the classical spectrum of the complex structure fields, and derive a new stability bound involving the compactification volume and the (very large) number of moduli. We also present a new class of vacua for this sector where the mass spectrum presents a finite gap, without invoking large supersymmetric masses. At these vacua the complex structure sector is protected from tachyonic instabilities even at non-exponential volumes. A distinguishing feature is that all fermions in this sector are lighter than the gravitino.

Figures (2)

• Figure 1: Scalar mass spectrum, \ref{['totaldensityM4']}, of the complex structure sector at tree-level with a large number of fields, $N\to \infty$. The spectrum is always tachyon-free, but when the heaviest fermion is heavier than the gravitino, $m_h>m_{3/2}$ (left), the spectral density diverges as $\rho(\mu^2) \sim 1/\mu$ near $\mu=0$. By contrast, if the heaviest fermion is lighter than the gravitino, $m_h<m_{3/2}$ (right), the stability of the configuration is protected by a gap in the mass spectrum of size $\mu_\text{min}^2 = (m_{3/2}- m_h)^2$.
• Figure 2: Percentage of (real) scalars in the complex structure sector with tree-level masses smaller than the size of the leading quantum corrections, $\mu^2 \le m_{3/2}^2 \cdot \hat{\xi}/{\cal V}$. The horizontal axis represents the typical mass scale in this sector, $m_h$. The spectrum of perturbations of the LSF vacua ($m_h< m_{3/2}$), contains no light scalar modes at tree-level. Stability is also ensured if there is a large hierarchy between the masses of the supersymmetric complex structure sector and the supersymmetry breaking scale, $m_h\gg m_{3/2}$ (KKLT regime), or an exponentially large volume, $\hat{\xi}/{\cal V} \sim 10^{-10}$ (LVS).