Infinite Distances in Field Space and Massless Towers of States

TL;DR

This paper provides evidence that infinite distances in Calabi-Yau moduli space correspond to an infinite tower of massless states, supporting the conjecture that such phenomena are emergent quantum effects in quantum gravity.

Contribution

It demonstrates that infinite distances are associated with infinite monodromy orbits generating massless BPS states and shows how the metric and gauge couplings emerge from integrating out these states.

Findings

Infinite distance points have infinite monodromy orbits.

Masses of states decrease exponentially near infinite distance.

Gauge couplings vanish as infinite towers of states are integrated out.

Abstract

It has been conjectured that in theories consistent with quantum gravity infinite distances in field space coincide with an infinite tower of states becoming massless exponentially fast in the proper field distance. The complex-structure moduli space of Calabi-Yau manifolds is a good testing ground for this conjecture since it is known to encode quantum gravity physics. We study infinite distances in this setting and present new evidence for the above conjecture. Points in moduli space which are at infinite proper distance along any path are characterised by an infinite order monodromy matrix. We utilise the nilpotent orbit theorem to show that for a large class of such points the monodromy matrix generates an infinite orbit within the spectrum of BPS states. We identify an infinite tower of states with this orbit. Further, the theorem gives the local metric on the moduli space which can be used to show that the mass of the states decreases exponentially fast upon approaching the point. We also propose a reason for why infinite distances are related to infinite towers of states. Specifically, we present evidence that the infinite distance itself is an emergent quantum phenomenon induced by integrating out at one-loop the states that become massless. Concretely, we show that the behaviour of the field space metric upon approaching infinite distance can be recovered from integrating out the BPS states. Similarly, at infinite distance the gauge couplings of closed-string Abelian gauge symmetries vanish in a way which can be matched onto integrating out the infinite tower of charged BPS states. This presents evidence towards the idea that also the gauge theory weak-coupling limit can be thought of as emergent.