Heterotic-type II duality in twistor space

Abstract

Heterotic string theory compactified on a K3 surface times T 2 is believed to be equivalent to type II string theory on a suitable Calabi-Yau threefold. In particular, it must share the same hypermultiplet moduli space. Building on the known twistorial description on the type II side, and on recent progress on the map between type II and heterotic moduli in the limit where both the type II and heterotic strings become classical, we provide a new twistorial construction of the hypermultiplet moduli space in this limit which is adapted to the symmetries of the heterotic string. We also take steps towards understanding the twistorial description for heterotic worldsheet instanton corrections away from the classical limit. As a spin-off, we obtain a twistorial description of a class of automorphic forms of SO(4, n, Z) obtained by Borcherds' lift.

On quantum corrected Kähler potentials in F-theory

“…Even within the realm of N = 2 compactifications, we have focused on the easier half of the problem, the vector multiplet moduli space. Recently there has been some remarkable work on the understanding of quantum corrections to the hypermultiplet moduli space [73][74][75][76][77][78][79][80][81][82][83][84][85][86][87] (see also [88] for a nice review of many of these results), and it would also be illuminating to carry over these results to the context of F-theory compactifications, as we have done here for the vector multiplet moduli space.…”

N = 2 heterotic-type II duality and bundle moduli

“…where Re s is the area of the base P of the K3 fibration, so the large volume limit ρ → −∞ on the heterotic side corresponds to g (4) → 0 and Re s → +∞ on the type IIB side. The ten-dimensional string coupling is however finite in this limit [20],…”

“…does depend on all Kähler moduli except s, and includes effects of all worldsheet instantons wrapping the two-cycles γ i , γ α , in addition to the classical cubic contribution, because the Kähler moduli t i , t α stay finite in the large volume limit ρ → −∞ on the heterotic side. In [19,20], it was shown that in the absence of reducible singular fibers, the QK metric derived from the leading term (3.3) describes the symmetric space SO(4, n)/SO(4) × SO(n), reproducing the expected hypermultiplet moduli space for heterotic strings compactified on K3 equipped with a rigid gauge bundle. Under this identification, the heterotic and type II variables were related by (3.1) supplemented by…”

“…Guided by similar definitions in the absence of bundle moduli t α [19,20], we further define the symmetric matrix…”

“…To this end, we assume that the type IIB ten-dimensional string coupling is weak (so that, on the heterotic side, the area of the elliptic fiber is much smaller than the base), and that the volume of S is large in heterotic string units (so that, on the type IIB side, the area of the base of the K3 fibration is also large in type II string units). In this regime, and in the special case of heterotic compactifications with a rigid bundle, a suitable duality map was constructed in [19,20], which identifies the hypermultiplet moduli space on the type IIB side (parametrizing the string coupling, Neveu-Schwarz axion, Kähler structures and associated RR-potentials) with the heterotic hypermultiplet moduli space.…”