Swampland Conjectures and Infinite Flop Chains

TL;DR

This paper explores the implications of swampland conjectures for M-theory compactifications with infinite flop chains, connecting geometric conjectures with quantum gravity constraints and resolving apparent conflicts in the moduli space structure.

Contribution

It demonstrates how swampland conjectures relate to the Kawamata-Morrison conjecture and clarifies the structure of moduli space in infinite flop chains.

Findings

Discrete symmetries relate isomorphic Calabi-Yau manifolds in finite flop chains.

Infinite non-isomorphic flop chains are ruled out if Kawamata-Morrison conjecture holds.

Swampland distance conjecture supports Kawamata-Morrison conjecture under certain conditions.

Abstract

We investigate swampland conjectures for quantum gravity in the context of M-theory compactified on Calabi-Yau threefolds which admit infinite sequences of flops. Naively, the moduli space of such compactifications contains paths of arbitrary geodesic length traversing an arbitrarily large number of K\"ahler cones, along which the low-energy spectrum remains virtually unchanged. In cases where the infinite chain of Calabi-Yau manifolds involves only a finite number of isomorphism classes, the moduli space has an infinite discrete symmetry which relates the isomorphic manifolds connected by flops. This is a remnant of the 11D Poincare symmetry and consequently gauged, as it has to be by the no-global symmetry conjecture. The apparent contradiction with the swampland distance conjecture is hence resolved after dividing by this discrete symmetry. If the flop sequence involves infinitely many non-isomorphic manifolds, this resolution is no longer available. However, such a situation cannot occur if the Kawamata-Morrison conjecture for Calabi-Yau threefolds is true. Conversely, the swampland distance conjecture, when applied to infinite flop chains, implies the Kawamata-Morrison conjecture under a plausible assumption on the diameter of the K\"ahler cones.