# University of Hertfordshire

## Subsectors, Dynkin Diagrams and New Generalised Geometries

Research output: Contribution to journalArticlepeer-review

### Standard

In: JHEP, Vol. 2017, No. 8, 144, 31.08.2017.

Research output: Contribution to journalArticlepeer-review

### Bibtex

@article{4fc8cd8deab24182a91868180cea03b5,
title = "Subsectors, Dynkin Diagrams and New Generalised Geometries",
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. ",
keywords = "hep-th, math.DG",
author = "Charles Strickland-Constable",
note = "{\textcopyright} The Author(s) 2017.",
year = "2017",
month = aug,
day = "31",
doi = "10.1007/JHEP08(2017)144",
language = "English",
volume = "2017",
journal = "JHEP",
number = "8",

}

### RIS

TY - JOUR

T1 - Subsectors, Dynkin Diagrams and New Generalised Geometries

AU - Strickland-Constable, Charles

N1 - © The Author(s) 2017.

PY - 2017/8/31

Y1 - 2017/8/31

N2 - 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.

AB - 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.

KW - hep-th

KW - math.DG

U2 - 10.1007/JHEP08(2017)144

DO - 10.1007/JHEP08(2017)144

M3 - Article

VL - 2017

JO - JHEP

JF - JHEP

IS - 8

M1 - 144

ER -