Large Volume Scenario from Schoen Manifold with de Sitter under Swampland Conjecture

Abstract

To naturally allow for string compactification with duality manifested, here we investigate in the self-mirror large volume scenarios from Schoen Calabi-Yau manifold. We explicitly study the geometry of Schoen Calabi-Yau threefold and complete its triple intersection from both ambient and non-ambient spaces. Based on these, we study the large volume scenario of self-mirror Calabi-Yau compactification with Schoen type. Moreover, by studying the leading non-perturbative terms of the effective scalar potential, we find special uplift terms in order of F-term $\mathcal{O}(\frac{1}{\mathcal{V}^2})$ arising from self-mirror large volume scenario. In particular, the quotient Schoen and Schoen Calabi-Yau large volume scenarios both give rise to de Sitter vacua. In addition, we discussed on the criteria to the effective scalar potential derived from self-mirror large volume scenario according to the swampland conjecture with the constraints fulfilled.

Figures (10)

• Figure 1: Total volume in Kähler moduli space according to $\tau_0, \tau_1$ and $\tau_2$.
• Figure 2: Total volume in Kähler moduli space according to $\tau_0, \tau_i^{(1)}$ and $\tau_j^{(2)}$.
• Figure 3: Self-mirror scalar potential $V$ according to $\tau_0$ and $\tau_1$ with numerical constant value of $W_0=1, A_0=1, a_0= 2 \pi, b_0= 1/4, \tau_1=10^7$. The potential ends with positive value approaching the large volume limit.
• Figure 4: Quotient Schoen scalar potential at the large volume limit $\tau_1, \tau_2\to \infty, a_0\tau_0\sim \ln \mathcal{V}$, according to $\tau_0$ and axionic field $b_0=[0, 1]$. Here the value $W_0=1,A_0=1, a_0=2\pi, \tau_1= 10^8, \tau_2= 10^8$ are used. The positive uplift term gives rise to de Sitter vacuum at saddle point region.
• Figure 5: Quotient Schoen scalar potential at the large volume limit $\tau_0 \to \infty$ while $a_1\tau_1, a_2\tau_2 \sim \ln \mathcal{V}$. $V$ is plotted as function of $\tau_2$ and axionic field $b_2=[0, 1]$ according to \ref{['SV']} with $W_0=1, A_1=1, A_2=1, a_1= 2\pi, a_2=2 \pi, \tau_0= 10^6, \tau_1= 3, b_1=1$. The de Sitter vacuum located along the $\tau_1, \tau_2$ directions as a saddle point.