Infinite distances in field space and massless towers of states

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.

De Sitter vs Quintessence in String Theory

“…If it is a pseudo‐scalar like an axion, it can avoid fifth‐force constraints, but a typical axion potential is flat enough to drive a period of accelerated expansion only if its decay constant is trans‐Planckian . This is in disagreement with recent studies of axion field ranges from string theory . On the other hand, if the quintessence field is a scalar, it is not clear how to avoid the existing stringent bounds from fifth‐forces .…”

“…In order to perform a proper study of the implications for quintessence, they have to be considered within a full moduli stabilisation mechanism. However, as mentioned above, one generically needs trans‐Planckian axionic decay constants to drive a period of accelerated expansion while recent studies of axion field ranges in string theory showed that this is very hard to achieve …”

The Swampland: Introduction and Review

“…Note that this shows that the Weak Gravity Conjecture is really a statement about non‐perturbative quantum gravity, it is violated in perturbative string theory. Studies of the Weak Gravity Conjecture in the context of closed‐string U (1)s were made in []. Note that some of these can also be considered studies of open‐string U (1)s, as considered in section 4.5.2, because at strong coupling the distinction becomes rather blurred.…”

“…Already for the spectrum of half‐BPS states in the theory (supersymmetric wrapped branes) depends on the position in moduli space. However, we will utilize a useful and general technique in section 4.7 that will allow to identify such a tower even for complicated geometries . The physics of it will actually play an important role throughout much of this review and so it is worth discussing in this simple setting first.…”

The Asymptotic dS Swampland Conjecture ‐ a Simplified Derivation and a Potential Loophole

“…In [] the authors also point out an interesting connection between their refined dS swampland conjecture and the swampland distance conjecture . They do so by using Bousso's covariant entropy bound and thereby provide support for their refined dS swampland conjecture in the asymptotic regime, which is parametrically controlled in a strict, mathematical sense.…”