Abstract
The Swampland Distance Conjecture proposes that approaching infinite distances in field space an infinite tower of states becomes exponentially light. We study this conjecture for the complex structure moduli space of Calabi-Yau manifolds. In this context, we uncover significant structure within the proposal by showing that there is a rich spectrum of different infinite distance loci that can be classified by certain topological data derived from an associated discrete symmetry. We show how this data also determines the rules for how the different infinite distance loci can intersect and form an infinite distance network. We study the properties of the intersections in detail and, in particular, propose an identification of the infinite tower of states near such intersections in terms of what we term charge orbits. These orbits have the property that they are not completely local, but depend on data within a finite patch around the intersection, thereby forming an initial step towards understanding global aspects of the distance conjecture in field spaces. Our results follow from a deep mathematical structure captured by the so-called orbit theorems, which gives a handle on singularities in the moduli space through mixed Hodge structures, and is related to a local notion of mirror symmetry thereby allowing us to apply it also to the large volume setting. These theorems are general and apply far beyond Calabi-Yau moduli spaces, leading us to propose that similarly the infinite distance structures we uncover are also more general.
Highlights
There are a number of proposed consistency constraints on effective quantum field theories that could potentially arise from string theory
In this paper we studied aspects of the Swampland Distance Conjecture in the complex structure moduli space of Calabi-Yau manifolds
We showed that any infinite distance point is part of a locus in moduli space to which we can associate a set of discrete topological data, its Hodge-Deligne diamond, that defines its key characteristics
Summary
There are a number of proposed consistency constraints on effective quantum field theories that could potentially arise from string theory. The distance conjecture has been studied in a number of different settings and utilising different approaches [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] It has been generalised and refined to a proposal which should hold for fields with a potential and for any super-Planckian variations in field space [3, 4]. In [12] such a systematic study was initiated for the complex structure moduli space of Calabi-Yau manifolds in compactifications of type IIB string theory to four dimensions We will retain this setting in this paper.. The conjecture was shown to hold for a large class of infinite distances without referring to any specific example The reason such a general approach is possible is because infinite distance loci in moduli space have some very general properties. In figure 3 we give a different example of an infinite distance network where we focus in on the
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