Subsectors, Dynkin Diagrams and New Generalised Geometries

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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.
Original languageEnglish
Article number144
Number of pages35
JournalJournal of High Energy Physics (JHEP)
Volume2017
Issue number8
Early online date31 Aug 2017
DOIs
Publication statusE-pub ahead of print - 31 Aug 2017

Keywords

  • hep-th
  • math.DG

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