M-theory moduli spaces and torsion-free structures

Abstract

Motivated by the description of N = 1 M-theory compactifications to fourdimensions given by Exceptional Generalized Geometry, we propose a way to geometrize the M-theory fluxes by appropriately relating the compactification space to a higherdimensional manifold equipped with a torsion-free structure. As a non-trivial example of this proposal, we construct a bijection from the set of Spin(7)-structures on an eightdimensional S 1 -bundle to the set of G 2 -structures on the base space, fully characterizing the G 2 -torsion clases when the total space is equipped with a torsion-free Spin(7)-structure. Finally, we elaborate on how the higher-dimensional manifold and its moduli space of torsion-free structures can be used to obtain information about the moduli space of Mtheory compactifications.

Internal circle uplifts, transversality and stratified G-structures

“…In full generality, the answer to this question is non-obvious, since the topology of sucĥ M would have to depend rather non-trivially on the topology of the stratified G-structure of M . Another interesting question is to find a physics interpretation of the interaction between uplifts, stratified G-structures and intersection theory which appears to govern many of the phenomena uncovered in this paper and in the closely related work of [31,32]. This requires further conceptual development on which we hope to report in future work.…”

“…A related problem is whether (as suggested by the results of [31,32]) one can find a compact manifoldM (of dimension higher than nine) which fibers over M , such that the stratified G-structure of M uplifts to a globally-defined reduction of structure group ofM . In full generality, the answer to this question is non-obvious, since the topology of sucĥ M would have to depend rather non-trivially on the topology of the stratified G-structure of M .…”

Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

“…Deformations of G 2 holonomy manifolds, and their associated moduli space, have been thoroughly studied, both by mathematicians and theoretical physicists [4][5][6][7][8][9][10] (see [11] for a recent review). It has been shown, by Joyce [4,5], that, for compact spaces, the third Betti number sets the dimension of the infinitesimal moduli space.…”

The Infinitesimal Moduli Space of Heterotic G 2 Systems

“…One can define a canonical differential complexΛ * (Y ) as a sub complex of the de Rham complex [32], and the associated cohomologiesȞ * (Y ) have similarities with the Dolbeault complex of complex geometry. Heterotic vacua on seven dimensional non-compact manifolds with an integrable G 2 structure lead to fourdimensional domain wall solution that are of interest in physics [33][34][35][36][37][38][39][40][41][42][43][44][45][46], and whose moduli determine the massless sector of the four-dimensional theory. Furthermore, families of SU (3) structure manifolds can be studied through an embedding in integrable G 2 geometry.…”

“…We find in particular, a G 2 analogue of Atiyah's deformation space for holomorphic systems [52]. We restrict ourselves in the current paper to scenarios where the internal geometry Y is compact, though we are confident that the analysis can also be applied in non-compact scenarios such as the domain wall solutions [33][34][35][36][37][38][39][40][41][42][43][44][45][46], provided suitable boundary conditions are imposed.…”