The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces

TL;DR

The authors test the Refined Swampland Distance Conjecture in Calabi–Yau Kahler moduli spaces by computing proper geodesic distances along trajectories that traverse geometric and non-geometric phases. They employ two complementary methods to obtain the Kahler metric: the sphere partition function of GLSMs and periods/mirror maps, allowing them to quantify distances across h11=1, 2, and 101 CYs. Across one-, two-, and high-dimensional moduli spaces, they find that finite non-geometric distances per phase are sub-Planckian, while infinite directions display the predicted logarithmic scaling of the proper distance, consistent with the RSDC. A key emergent pattern is that the finite distance per phase appears to shrink as the number of phases grows, preserving the conjecture’s bound and supporting its universality in CY moduli spaces.

Abstract

The Swampland Distance Conjecture claims that effective theories derived from a consistent theory of quantum gravity only have a finite range of validity. This will imply drastic consequences for string theory model building. The refined version of this conjecture says that this range is of the order of the naturally built in scale, namely the Planck scale. It is investigated whether the Refined Swampland Distance Conjecture is consistent with proper field distances arising in the well understood moduli spaces of Calabi-Yau compactification. Investigating in particular the non-geometric phases of Kahler moduli spaces of dimension $h^{11}\in\{1,2,101\}$, we always found proper field distances that are smaller than the Planck-length.

Figures (15)

• Figure 1: Sketch of the Kähler moduli space of the quintic.
• Figure 2: Expected relation between proper field distance $\Theta$ and ${\rm Im} \, t$.
• Figure 3: Plot of ${G^{1/ 2}_{\psi\overline \psi}(r,\theta)}$. Dashed line: up to order $r^6$. Solid upper line: up to order $r^{100}$ for $\theta=0$. Solid lower line: up to order $r^{100}$ for $\theta={2\pi\over 10}$.
• Figure 4: The metric on the Kähler moduli space of the quintic.
• Figure 5: Geodesics for the initial data $(r,\dot{r},\theta,\dot{\theta})=(0,1,i\cdot\pi/50,0)$, for $i=1,\dots,10$. The orange geodesics are the $\mathbb{Z}_2$ images.