Exceptional Calabi–Yau spaces: the geometry of backgrounds with flux

168

We study D ≥ 4-dimensional half-maximal flux backgrounds using exceptional field theory. We define the relevant generalised structures and also find the integrability conditions which give warped half-maximal Minkowski D and AdS D vacua. We then show how to obtain consistent truncations of type II / 11-dimensional SUGRA which break half the supersymmetry. Such truncations can be defined on backgrounds admitting exceptional generalised SO(d−1−N ) structures, where d = 11−D, and N is the number of vector multiplets obtained in the lower-dimensional theory. Our procedure yields the most general embedding tensors satisfying the linear constraint of half-maximal gauged SUGRA. We use this to prove that all D ≥ 4 half-maximal warped AdS D and Minkowski D vacua of type II / 11-dimensional SUGRA admit a consistent truncation keeping only the gravitational supermultiplet. We also show to obtain heterotic double field theory from exceptional field theory and comment on the M-theory / heterotic duality. In five dimensions, we find a new SO(5, N ) double field theory with a (6 + N )-dimensional extended space. Its section condition has one solution corresponding to 10-dimensional N = 1 supergravity and another yielding six-dimensional N = (2, 0) SUGRA.

“…As we will show elsewhere, one can understand the above relations as the vanishing of certain moment maps. This is similar to the integrability conditions of N = 2 flux vacua [87].…”

Section: Half-maximal Minkowski and Ads Vacuasupporting

confidence: 79%

“…Similar to the N = 2 case [87], and as we will discuss elsewhere, this is related to certain moment maps vanishing.…”

Section: Intrinsic Torsion Of Dilaton Structurementioning

confidence: 63%

Section: Discussionmentioning

confidence: 99%

“…where κ there refers to the scalar density in [87]. Next, recall that from the 4 J u 's one can define generators of the SO(4) N =4 R symmetry as…”

Section: Relation To N = 2 Structuresmentioning

confidence: 99%

Section: Relation To N = 2 Structuresmentioning

confidence: 99%

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Half‐Maximal Supersymmetry from Exceptional Field Theory

Malek

2017

168

Pre‐NQ Manifolds and Correspondence Spaces: the Nilmanifold Example

Deser

2019

Courant algebroids correspond to degree‐2 symplectic differential graded manifolds or NQ‐manifolds for short. We review how a similar construction shows that locally the gauge structure of Double Field Theory corresponds to degree‐2 symplectic pre‐NQ manifolds. To illustrate first steps towards a global understanding of the pre‐NQ case, we apply the local constructions to 3‐dimensional nilmanifolds carrying an abelian gerbe. These are among prime examples where T‐duality is well‐understood and allow us to investigate classic results in the graded language.

Supergravity Fluxes and Generalised Geometry

Strickland‐Constable

2019

We briefly review the description of the internal sector of supergravity theories in the language of generalised geometry and how this gives rise to a description of supersymmetric backgrounds as integrable geometric structures. We then review recent work, featuring holomorphic Courant algebroids, on the description of N=1 heterotic flux vacua. This work studied the finite deformation problem of the Hull–Strominger system, guided by consideration of the superpotential functional on the relevant space of geometries. It rewrote the system in terms of the Maurer–Cartan set of a particular L∞‐algebra associated to a holomorphic Courant algebroid, with the superpotential itself becoming an analogue of a holomorphic Chern–Simons functional.