# Supergravity as generalised geometry I: type II theories

@article{Coimbra2011SupergravityAG, title={Supergravity as generalised geometry I: type II theories}, author={Andr'e Coimbra and C. Strickland-constable and Daniel Waldram}, journal={Journal of High Energy Physics}, year={2011}, volume={2011}, pages={1-35} }

A bstractWe reformulate ten-dimensional type II supergravity as a generalised geometrical analogue of Einstein gravity, defined by an O(9, 1) × O(1, 9) ⊂ O(10, 10) × $ {\mathbb{R}^{+} } $ structure on the generalised tangent space. Using the notion of generalised connection and torsion, we introduce the analogue of the Levi-Civita connection, and derive the corresponding tensorial measures of generalised curvature. We show how, to leading order in the fermion fields, these structures allow one… Expand

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#### References

SHOWING 1-10 OF 58 REFERENCES

M-theory, exceptional generalised geometry and superpotentials

- Physics, Mathematics
- 2008

We discuss the structure of "exceptional generalised geometry" (EGG), an extension of Hitchin's generalised geometry that provides a unified geometrical description of backgrounds in… Expand

An Exceptional geometry for D = 11 supergravity?

- Physics
- 2000

We analyse the algebraic constraints of the generalized vielbein in SO(1,2)×SO(16) invariant d = 11 supergravity, and show that the bosonic degrees of freedom of d = 11 supergravity, which become the… Expand

Generalised G2-structures and type IIB superstrings

- Physics
- 2005

The recent mathematical literature introduces generalised geometries which are defined by a reduction from the structure group SO(d,d) of the vector bundle Td⊕Td* to a special subgroup. In this… Expand

Supersymmetric backgrounds from generalized Calabi‐Yau manifolds

- Physics, Mathematics
- 2005

We show that the supersymmetry transformations for type II string theories on six-manifolds can be written as differential conditions on a pair of pure spinors, the exponentiated Kahler form eiJ and… Expand

Supersymmetric backgrounds from generalized Calabi-Yau manifolds

- Physics
- 2004

We show that the supersymmetry transformations for type II string theories on six-manifolds can be written as differential conditions on a pair of pure spinors, the exponentiated Kahler form eiJ and… Expand

E-11, generalised space-time and IIA string theory

- Physics
- 2011

Abstract As advocated in hep-th/0307098 we construct the non-linear realisation of the semi-direct product of E 11 and its first fundamental representation at lowest level from the IIA viewpoint. We… Expand

Double field theory of type II strings

- Physics
- 2011

We use double field theory to give a unified description of the low energy limits of type IIA and type IIB superstrings. The Ramond-Ramond potentials fit into spinor representations of the duality… Expand

Generalised geometry for M-theory

- Physics, Mathematics
- 2007

Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d, d). This is generalised to d-dimensional… Expand

T-duality, generalized geometry and non-geometric backgrounds

- Physics
- 2009

We discuss the action of O(d,d), and in particular T-duality, in the context of generalized geometry, focusing on the description of so-called non-geometric backgrounds. We derive local expressions… Expand

Generalized geometry and M theory

- Physics
- 2010

We reformulate the Hamiltonian form of bosonic eleven dimensional supergravity in terms of an object that unifies the three-form and the metric. For the case of four spatial dimensions, the duality… Expand