On nearly parallel G2-structures

Friedrich, Thomas; Kath, Ines; Moroianu, Andrei; Semmelmann, Uwe

doi:10.1016/s0393-0440(97)80004-6

Cited by 169 publications

(189 citation statements)

References 12 publications

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“…Since the other spinors ǫ A are not Killing for the deformed metric, the resulting space carries a strict nearly parallel G 2 -structure [32]. See below for the deformation.…”

Section: -Sasakianmentioning

confidence: 99%

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Instantons and Killing spinors

Harland

Nölle

2012

J. High Energ. Phys.

229

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We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kähler 6-manifolds, nearly parallel G2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds. We construct a connection on the tangent bundle over these manifolds which solves the instanton equation, and also show that the instanton equation implies the Yang-Mills equation, despite the presence of torsion. We then construct instantons on the cones over these manifolds, and lift them to solutions of heterotic supergravity. Amongst our solutions are new instantons on even-dimensional Euclidean spaces, as well as the well-known BPST, quaternionic and octonionic instantons.

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“…Since the other spinors ǫ A are not Killing for the deformed metric, the resulting space carries a strict nearly parallel G 2 -structure [32]. See below for the deformation.…”

Section: -Sasakianmentioning

confidence: 99%

“…Two other special h-values are h = 0 and exp(2h) = 2m + 3; both metrics are Einstein, but only the first is 3-Sasakian. In dimension 7 the metric with exp(2h) = 5 is nearly parallel G 2 [32].…”

Section: -Sasakianmentioning

confidence: 99%

Instantons and Killing spinors

Harland

Nölle

2012

J. High Energ. Phys.

229

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“…We set d = 3, and the spacetime SUSY requires the condition 15) where U(1) 3/2 denotes a c = 1 CFT whose conformal blocks are described by characters Θ * ,3/2 (τ )/η(τ ). Precisely this relation means that the conformal blocks of the M-sector are expanded in terms of characters Θ * ,3/2 (τ )/η(τ ) and the branching coefficients are not hit by the GSO projection.…”

Section: General Set Up and Aspects Of Spacetime Susymentioning

confidence: 99%

“…Einstein metric that provides a weak G 2 holonomy [13,15] (see also [8,12]). A way to present the squashing procedure is to replace the original tri-Sasakian coset G/H…”

Section: G/h = (Su(2) × Su(2))/su(2)mentioning

confidence: 99%

“…This fact is very useful to systematically construct special holonomy manifolds with conical singularities, because the Einstein homogeneous spaces X m−1 = G/H endowed with these geometrical structures are well understood since the old days of Kaluza-Klein supergravity (SUGRA) [17][18][19][20][21][22][23] (and [24] for a review) as well as from the mathematical literature mentioned above [11][12][13][14][15][16] and [25].…”

Section: Introductionmentioning

confidence: 99%

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Supercoset CFTs for string theories on non-compact special holonomy manifolds

Sugawara

Yamaguchi

2003

Nuclear Physics B

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We study aspects of superstring vacua of non-compact special holonomy manifolds with conical singularities constructed systematically using soluble N = 1 superconformal field theories (SCFT's). It is known that Einstein homogeneous spaces G/H generate Ricci flat manifolds with special holonomies on their cones ≃ R + × G/H, when they are endowed with appropriate geometrical structures, namely, the Sasaki-Einstein, triSasakian, nearly Kähler, and weak G 2 structures for SU(n), Sp(n), G 2 , and Spin (7) holonomies, respectively. Motivated by this fact, we consider the string vacua of the type:where we use the affine Lie algebras of G and H in order to capture the geometry associated to an Einstein homogeneous space G/H. Remarkably, we find the same number of spacetime and worldsheet SUSY's in our "CFT cone" construction as expected from the analysis of geometrical cones over G/H in many examples. We also present an analysis on the possible Liouville potential terms (cosmological constant type operators) which provide the marginal deformations resolving the conical singularities.

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Purely coclosed G₂‐structures on nilmanifolds

Bazzoni

Garvı́n

Muñoz

2023

Mathematische Nachrichten

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We classify seven‐dimensional nilpotent Lie groups, decomposable or of nilpotency step at most 4, endowed with left‐invariant purely coclosed G2‐structures. This is done by going through the list of all seven‐dimensional nilpotent Lie algebras given by Gong, providing an example of a left‐invariant 3‐form φ which is a pure coclosed G2‐structure (i.e., it satisfies d∗φ=0$d*\varphi =0$, φ∧dφ=0$\varphi \wedge d\varphi =0$) for those nilpotent Lie algebras that admit them; and by showing the impossibility of having a purely coclosed G2‐structure for the rest of them.

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On nearly parallel G2-structures

Cited by 169 publications

References 12 publications

Instantons and Killing spinors

Instantons and Killing spinors

Supercoset CFTs for string theories on non-compact special holonomy manifolds

Purely coclosed G₂‐structures on nilmanifolds

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On nearly parallel G2-structures

Cited by 169 publications

References 12 publications

Instantons and Killing spinors

Instantons and Killing spinors

Supercoset CFTs for string theories on non-compact special holonomy manifolds

Purely coclosed G2‐structures on nilmanifolds

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Product

Resources

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Purely coclosed G₂‐structures on nilmanifolds