Exceptional complex structures and the hypermultiplet moduli of 5d Minkowski compactifications of M-theory

A bstract We present a detailed study of new mathematical object in E 6(6) ℝ + generalised geometry called an ‘exceptional complex structure’ (ECS). It is the extension conventional structure to one that includes all degrees freedom M-theory or type IIB supergravity six five dimensions, and as such characterises, part, generic supersymmetric compactifications five-dimensional Minkowkski space. define ECS integrable U * (6) × show it equivalent particular form involutive subbundle complexified tangent bundle L 1 ⊂ ℂ . also refinement, SU structure, its integrability requires addition vanishing moment map on space structures. are able classify possible ECSs, showing they characterised by two numbers denoted ‘type’ ‘class’. then use deformation theory find moduli any structure. relate these structures minimally flux backgrounds 4 , M where correspond hypermultiplet lower-dimensional theory. Such geometries class zero one. The former choice (non-metric-compatible) SL(3 ℂ) strikingly have same fluxless Calabi-Yau case.