Restrictions on infinite sequences of type IIB vacua

TL;DR

This paper refines the understanding of the finiteness of type IIB flux vacua, showing that infinite sequences do not accumulate at certain moduli space points, and confirms the finiteness of vacua near the large complex structure point through both analytical and numerical methods.

Contribution

It analytically proves the absence of infinite flux vacua sequences near specific moduli space points for certain Calabi-Yau manifolds and numerically confirms the finiteness of vacua series.

Findings

No infinite sequences near large complex structure points for certain Calabi-Yau manifolds.

Series of vacua are finite and bounce away from the large complex structure point.

Infinite sequences in F-theory on K3×K3 are related to automorphisms, not accumulation points.

Abstract

Ashok and Douglas have shown that infinite sequences of type IIB flux vacua with imaginary self-dual flux can only occur in so-called D-limits, corresponding to singular points in complex structure moduli space. In this work we refine this no-go result by demonstrating that there are no infinite sequences accumulating to the large complex structure point of a certain class of one-parameter Calabi-Yau manifolds. We perform a similar analysis for conifold points and for the decoupling limit, obtaining identical results. Furthermore, we establish the absence of infinite sequences in a D-limit corresponding to the large complex structure limit of a two-parameter Calabi-Yau. In particular, our results demonstrate analytically that the series of vacua recently discovered by Ahlqvist et al., seemingly accumulating to the large complex structure point, are finite. We perform a numerical study of these series close to the large complex structure point using appropriate approximations for the period functions. This analysis reveals that the series bounce out from the large complex structure point, and that the flux eventually ceases to be imaginary self-dual. Finally, we study D-limits for F-theory compactifications on K3\times K3 for which the finiteness of supersymmetric vacua is already established. We do find infinite sequences of flux vacua which are, however, identified by automorphisms of K3.