M-theory moduli from exceptional complex structures

• Published in: The journal of high energy physics Vol. 2023; no. 8; pp. 22 - 37
• Main Authors: Smith, George Robert, Waldram, Daniel
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 07.08.2023; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Differential and Algebraic Geometry; Elementary Particles; Flux Compactifications; Geometry; High energy physics; Homology; M theory; Mathematical analysis; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Superstring Vacua; Superstring Vacua; Differential and Algebraic Geometry; Flux Compactifications; M-Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2023)022

A bstract We continue the analysis of the geometry of generic Minkowski N = 1, D = 4 flux compactifications in M-theory using exceptional generalised geometry, including the calculation of the infinitesimal moduli spaces. The backgrounds can be classified into two classes: type-0 and type-3. For type-0, we review how the moduli arise from standard de Rham cohomology classes. We also argue that, under reasonable assumptions, there are no appropriate sources to support compact flux backgrounds for this class and so the only solutions are in fact G 2 geometries. For type-3 backgrounds, given a suitable ∂ ′ ∂ ¯ ′ -lemma, we show that the moduli can be calculated from a cohomology based on an involutive sub-bundle of the complexified tangent space. Using a simple spectral sequence we prove quite generally that the presence of flux can only reduce the number of moduli compared with the fluxless case. We then use the formalism to calculate the moduli of heterotic M-theory and show they match those of the dual Hull-Strominger system as expected.