The intrinsic torsion of SU(3) and G_2 structures

By S. Chiossi, S. Salamon. 2002

437 citations recorded by the source corpus.

We analyse the relationship between the components of the intrinsic torsion of an SU(3) structure on a 6-manifold and a G_2 structure on a 7-manifold. Various examples illustrate the type of SU(3) structure that can arise as a reduction of a metric with holonomy G_2.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/567dabee082e22d5fdbebff1deff585cb6f0e026

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In Applied Mathematics

1. J. Sparks
2. D. Martelli
3. M. Graña
4. D. Waldram
5. J. Gauntlett
6. Anna Fino
7. M. Petrini
8. A. Tomasiello

In Geometry and Topology

1. M. Graña
2. J. Sparks
3. D. Martelli
4. D. Waldram
5. Paul Koerber
6. A. Tomasiello
7. J. Gauntlett
8. D. Lust

Citations in the corpus

• A scan for new N = 1 vacua on twisted tori (2006, background): “The other direction of the implication is less obvious (see for example [45]).”
• Mirror Symmetric SU(3)-Structure Manifolds with NS Fluxes (2003, background): “In the G2 geometry, 14 is such a representation, and the corresponding component of the torsion is the lifting of W− 2 [17, 21], the component of SU(3)-torsion central in the exchange with the NS flux.”
• De Sitter hunting in a classical landscape (2011, background): “,W5 correspond to the expansion of the exterior derivatives of J and Ω in terms of SU(3)-representations [77].”
• G structures, fluxes and calibrations in M theory (2003, background): “As discussed in [7] the six-dimensional slices at fixed y and z have an SU(3) structure with intrinsic torsion lying in the class W2 ⊕ W4 ⊕W5 with warp-factor 6 d6∆ = −W4 = W5 (see [48, 7] for details about the intrinsic torsion of SU(3) structures).”
• Mirror symmetry in generalized Calabi–Yau compactifications ☆ (2002, background): “If the holonomy group is trivial all 32 supercharges are preserved while SO(6) (or any subgroup thereof) breaks all (or some) of the supercharges.”
• SU(3) × SU(3) compactification and mirror duals of magnetic fluxes (2006, background): “More precisely, a Calabi-Yau compactification with electric NS three-form flux is conjectured to be mirror symmetric to compactifications on manifolds known as “half-flat manifolds” [3, 7, 11].”
• Families of strong KT structures in six dimensions (2002, background): “The terms on the right-hand side of (41) can be identified with the respective intrinsic torsion components W5,W4 [5].”
• Topological M-theory as unification of form theories of gravity (2004, background): “Its SU(3) representation content involves five classes, usually denoted Wi [86,87]: T ∈ W1 ⊕W2 ⊕W3 ⊕W4 ⊕W5.”
• Geometric Model for Complex Non-Kähler Manifolds with SU (3) Structure (2002, background): “The intrinsic torsion of the SU(3) structures falls into five different classes W1⊕W2⊕W3⊕W4⊕W5 (see [20, 4]).”
• Hitchin functionals in N = 2 supergravity (2005, background): “Manifolds with this property are known as ‘manifolds with SU (3) structure’ in the mathematical literature [44].”
• Supersymmetric AdS(4) compactifications of IIA supergravity (2004, background): “The following example, given in [15], of dynamic half-flat SU(3) structure is based on the Iwasawa manifold M.”
• Homogeneous nearly K\"{a}hler manifolds (2006, background): “At the geometric level, Salamon and Chiossi [13] have shown that the 1-jet of the SU(3)-structure (or the intrinsic torsion) is completely determined by the differentials of ω, ψ, φ.”
• Generalized N=1 orientifold compactifications and the Hitchin functionals (2006, background): “In case thatM6 has exactly one globally defined spinor the structure group of the manifold reduces to SU(3) [29, 30, 31].”