# University of Hertfordshire

## Subsectors, Dynkin Diagrams and New Generalised Geometries

Research output: Contribution to journalArticle

### Documents

Original language English 144 35 JHEP 2017 8 31 Aug 2017 https://doi.org/10.1007/JHEP08(2017)144 E-pub ahead of print - 31 Aug 2017

### Abstract

We examine how generalised geometries can be associated with a labelled Dynkin diagram built around a gravity line. We present a series of new generalised geometries based on the groups $\mathit{Spin}(d,d)\times\mathbb{R}^+$ for which the generalised tangent space transforms in a spinor representation of the group. In low dimensions these all appear in subsectors of maximal supergravity theories. The case $d=8$ provides a geometry for eight-dimensional backgrounds of M theory with only seven-form flux, which have not been included in any previous geometric construction. This geometry is also one of a series of "half-exceptional" geometries, which "geometrise" a six-form gauge field. In the appendix, we consider examples of other algebras appearing in gravitational theories and give a method to derive the Dynkin labels for the "section condition" in general. We argue that generalised geometry can describe restrictions and subsectors of many gravitational theories.