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.
Highlights
When studying string-derived models for particle physics and cosmology, an important question is which features are universally present and which ones are universally excluded
We have discussed the relation between topological transitions, flops, in string theory and the swampland distance conjecture
We were motivated by recent results [22,23] which show that infinite chains of CY flops are possible but are, a common feature of relatively simple constructions of CY manifolds
Summary
When studying string-derived models for particle physics and cosmology, an important question is which features are universally present and which ones are universally excluded. (iii) Infinite chains of flops arise frequently and even for relatively simple manifolds It is the last of these features which is the impetus for this present study of the swampland distance conjecture. Infinite chains of flop transitions seem to imply the existence of infinite-length geodesics, traversing an arbitrary number of Kähler cones but with the low-energy spectrum virtually unchanged This appears to contradict the swampland distance conjecture. For infinite chains of type (1) we establish the existence of an infinite discrete symmetry on the moduli space which must be gauged, and determine the source of this gauging Dividing by this symmetry leaves only a finite number of inequivalent Kähler cones and this removes any possible conflict with the swampland distance conjecture.
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