M-theory moduli from exceptional complex structures

George R. Smith

doi:10.1007/JHEP08(2023)022

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M-theory moduli from exceptional complex structures

2023-08-07

George R. Smith *

Daniel Waldram

DOI：10.1007/JHEP08(2023)022

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Abstract

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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 partial derivative'(partial derivative) over bar' -lemma, we show that the moduli can be calculated from a cohomology based on an involutive subbundle 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.

Keywords:

Flux Compactifications

Differential and Algebraic Geometry

M-Theory

Superstring Vacua