Moduli-dependent KK towers and the swampland distance conjecture on the quintic Calabi-Yau manifold

TL;DR

This paper numerically investigates the moduli-dependent Kaluza-Klein spectrum on the quintic Calabi-Yau, confirming the swampland distance conjecture by showing an exponential lightening of states with distance in moduli space.

Contribution

It provides the first detailed numerical analysis of moduli-dependent KK towers on the quintic Calabi-Yau and tests the swampland distance conjecture quantitatively.

Findings

KK spectrum varies with moduli and exhibits level-crossing.

Massive states become exponentially light with geodesic distance.

States in smaller symmetry representations tend to be lighter.

Abstract

We use numerical methods to obtain moduli-dependent Calabi-Yau metrics and from them the moduli-dependent massive tower of Kaluza-Klein states for the one-parameter family of quintic Calabi-Yau manifolds. We then compute geodesic distances in their K\"ahler and complex structure moduli space using exact expressions from mirror symmetry, approximate expressions, and numerical methods and compare the results. Finally, we fit the moduli-dependence of the massive spectrum to the geodesic distance to obtain the rate at which states become exponentially light. The result is indeed of order one, as suggested by the swampland distance conjecture. We also observe level-crossing in the eigenvalue spectrum and find that states in small irreducible representations of the symmetry group tend to become lighter than states in larger irreducible representations.