Emergent Strings from Infinite Distance Limits

TL;DR

This paper refines the Swampland Distance Conjecture by classifying infinite distance limits in Calabi-Yau moduli space, showing they lead to decompactification or emergent tensionless strings, with detailed analysis of M-Theory and Type IIA compactifications.

Contribution

It provides a detailed classification of infinite distance limits in Calabi-Yau moduli space and their implications for emergent strings or decompactification in string theory.

Findings

Infinite distance limits correspond to fibrations with shrinking fibers.

Depending on the fibration, limits lead to decompactification or tensionless strings.

Quantum effects restrict certain infinite distance limits in Type IIA theory.

Abstract

As a refinement of the Swampland Distance Conjecture, we propose that a quantum gravitational theory in an infinite distance limit of its moduli space either decompactifies, or reduces to an asymptotically tensionless, weakly coupled string theory. We support our claim by classifying, as special cases, the behaviour of M-Theory and Type IIA string theory compactifications on Calabi-Yau three-folds at infinite distances in Kahler moduli space. The analysis comprises three parts: We first classify the possible infinite distance limits in the classical Kahler moduli space of a Calabi-Yau three-fold. Each such limit at finite volume is characterized by a universal fibration structure, for which the generic fiber shrinking in the limit is either an elliptic curve, a K3 surface, or an Abelian surface. In the second part we focus on M-Theory and investigate the nature of the towers of asymptotically massless states that arise from branes wrapped on the shrinking fibers. Depending on which of the three classes of fibrations are considered, we obtain decompactification to F-Theory, or a theory with a unique asymptotically tensionless, weakly coupled heterotic or Type II string, respectively. The latter probes a dual D-manifold which is in general non-geometric. In addition to the intrinsic string excitations, towers of states from M2-branes along non-contractible curves become light and correspond to further wrapping and winding modes of the tensionless heterotic or Type II string. In the third part of the analysis, we consider Type IIA string theory on Calabi-Yau three-folds and show that quantum effects obstruct taking finite volume infinite distance limits in the Kahler moduli space. The only possible infinite distance limit which is not a decompactification limit involves K3-fibrations with string scale fiber volume and gives rise to an emergent tensionless heterotic string.