Spaces admitting homogeneous <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mi>G</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>-structures

Reidegeld, Frank

doi:10.1016/j.difgeo.2009.10.013

Cited by 14 publications

(10 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As X is constant, note that for generic 4-forms Y this defines a nearly-parallel G 2 -structure on M 7 , see e.g. [33] for homogeneous G 2 structures. However, in what follows we shall not assume that Y is generic.…”

Section: N = 20mentioning

confidence: 99%

AdS4 backgrounds with N > 16 supersymmetries in 10 and 11 dimensions

Haupt

Lautz

Papadopoulos

2018

J. High Energ. Phys.

View full text Add to dashboard Cite

We explore all warped AdS 4 × w M D−4 backgrounds with the most general allowed fluxes that preserve more than 16 supersymmetries in D = 10-and 11-dimensional supergravities. After imposing the assumption that either the internal space M D−4 is compact without boundary or the isometry algebra of the background decomposes into that of AdS 4 and that of M D−4 , we find that there are no such backgrounds in IIB supergravity. Similarly in IIA supergravity, there is a unique such background with 24 supersymmetries locally isometric to AdS 4 × CP 3 , and in D = 11 supergravity all such backgrounds are locally isometric to the maximally supersymmetric AdS 4 × S 7 solution.

show abstract

Section: N = 20mentioning

confidence: 99%

AdS4 backgrounds with N > 16 supersymmetries in 10 and 11 dimensions

Haupt

Lautz

Papadopoulos

2018

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…We find that such a P only exists if p = ±q, q = ±r and without loss of generality, we may restrict to the case p = q = r = 1. This observation is a manifestation of the well-known fact that only Q 111 admits an (SU (2)) 3 -invariant G 2 -structure [44,49].…”

Section: Cylinders Overmentioning

confidence: 85%

“…However, we will now encounter a crucial difference in comparison to the coset spaces studied in sections 3.5.1 and 3.5.2, namely that P abc ∝ f abc does not lead to a well-defined G 2 -structure on SO(5)/SO(3) A+B . This assertion can be verified inter alia by computing the so-called associated metric (see for example [41][42][43][44]),…”

Section: Cylinders Over So(5)/so(3) A+bmentioning

confidence: 96%

Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with G 2-structure

Haupt

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

We study g-valued Yang-Mills fields on cylinders Z(G/H) = R × G/H, where G/H is a compact seven-dimensional coset space with G 2 -structure, g is the Lie algebra of G, and Z(G/H) inherits a Spin(7)-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on Z(G/H) reduces to Newtonian mechanics of a point particle moving in R n under the influence of some quartic potential and possibly additional constraints. The kinematics and dynamics depends on the chosen coset space. We consider in detail three coset spaces with nearly parallel G 2 -structure and four coset spaces with SU (3)-structure. For each case, we analyze the critical points of the potential and present a range of finite-energy solutions. We also study a higher-dimensional analog of the instanton equation. Its solutions yield G-invariant Spin(7)-instanton configurations on Z(G/H), which are special cases of Yang-Mills configurations with torsion.

show abstract

“…The complete examples produced by Bryant & Salamon have many symmetries, in fact the symmetry group acts with cohomogeneity one, so the principal orbit is of codimension one. Further systematic study of cohomogeneity one examples with compact symmetry group has been made by Reidegeld [34,35]. One sees that many of the examples and candidates have compact symmetry groups of rank 3, so an interesting class of Spin(7)-manifolds are those with T 3 -symmetry.…”

Section: Holonomy Spin(7)mentioning

confidence: 99%

Closed forms and multi-moment maps

Madsen

Swann

2012

Geom Dedicata

View full text Add to dashboard Cite

We extend the notion of multi-moment map to geometries defined by closed forms of arbitrary degree. We give fundamental existence and uniqueness results and discuss a number of essential examples, including geometries related to special holonomy. For forms of degree four, multi-moment maps are guaranteed to exist and are unique when the symmetry group is (3,4)-trivial, meaning that the group is connected and the third and fourth Lie algebra Betti numbers vanish. We give a structural description of some classes of (3,4)-trivial algebras and provide a number of examples.Comment: 36 page

show abstract

Spaces admitting homogeneous G2-structures

Cited by 14 publications

References 15 publications

AdS4 backgrounds with N > 16 supersymmetries in 10 and 11 dimensions

AdS4 backgrounds with N > 16 supersymmetries in 10 and 11 dimensions

Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with G 2-structure

Closed forms and multi-moment maps

Contact Info

Product

Resources

About