Exploring $SU(3)$ structure moduli spaces with integrable $G_2$ structures

Abstract

Abstract:We study the moduli space of SU (3) structure manifolds X that form the internal compact spaces in four-dimensional N = 1 2 domain wall solutions of heterotic supergravity with flux. Together with the direction perpendicular to the four-dimensional domain wall, X forms a non-compact 7-manifold Y with torsionful G 2 structure. We use this G 2 embedding to explore how X(t) varies along paths C(t) in the SU (3) structure moduli space. Our analysis includes the Bianchi identities which strongly constrain the flow. We show that requiring that the SU (3) structure torsion is preserved along the path leads to constraints on the G 2 torsion and the embedding of X in Y . Furthermore, we study flows along which the torsion classes of X go from zero to non-zero values. In particular, we present evidence that the flow of half-flat SU (3) structures may contain Calabi-Yau loci, in the presence of non-vanishing H-flux.arXiv:1409.7539v2 [hep-th]

Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

“…The contractions between ϕ and ψ can be found in a number of references, see for example [61]. More useful relations can be found in [33] ϕ abc ϕ abc = 42 , (A.1)…”

“…2 In this paper, we will focus on this topic. Our study follows up on our recent paper [33], where the moduli space of certain six-dimensional SU(3) structure manifolds was explored using an embedding manifold with G 2 structure. Here, we take a different perspective and study the moduli space of G 2 holonomy manifolds together with that of a vector bundle that encodes the heterotic gauge field.…”

Generalised geometry and flux vacua

“…[52,53]. Recent work in this area also includes studies of the moduli of heterotic and M-theory compactifications, such as [54][55][56][57].…”

M-theory moduli spaces and torsion-free structures

“…Note that proposition 3.10 implies that ϕ satisfies 30) and thus τ 2 is a closed two-form. In fact, since τ 2 ∈ Ω 2 14 M 8 /S 1 it has to satisfy the constraint 31) and hence applying the exterior derivative we obtain that d * τ 2 = 0, so τ 2 is closed and coclosed and thus…”

“…Other examples of torsion-free structures dual to configuration with fluxes, in other words, non-zero torsion, can be found in references [25][26][27][28], this time from six-dimensions to a G 2 -holonomy. For further examples and results in the Spin(7) and G 2 cases see reference [29,30]. 10 Meaning the moduli space of torsion-free Spin(7) structures on M8.…”