scholarly journals Geometry of G-Structures via the Intrinsic Torsion

2016 ◽  
Author(s):  
Kamil Niedziałomski ◽  
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◽  
◽  
◽  
...  
Keyword(s):  
Intrinsic Torsion

scholarly journals $$ \mathcal{N} $$ = 2 consistent truncations from wrapped M5-branes

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Davide Cassani ◽  
Grégoire Josse ◽  
Michela Petrini ◽  
Daniel Waldram
Keyword(s):  
Riemann Surface ◽  
Gauge Group ◽  
Tangent Bundle ◽  
Dimensional Manifold ◽  
Five Dimensions ◽  
Intrinsic Torsion ◽  
Consistent Truncations

Abstract We discuss consistent truncations of eleven-dimensional supergravity on a six-dimensional manifold M, preserving minimal $$ \mathcal{N} $$ N = 2 supersymmetry in five dimensions. These are based on GS ⊆ USp(6) structures for the generalised E6(6) tangent bundle on M, such that the intrinsic torsion is a constant GS singlet. We spell out the algorithm defining the full bosonic truncation ansatz and then apply this formalism to consistent truncations that contain warped AdS5×wM solutions arising from M5-branes wrapped on a Riemann surface. The generalised U(1) structure associated with the $$ \mathcal{N} $$ N = 2 solution of Maldacena-Nuñez leads to five-dimensional supergravity with four vector multiplets, one hypermultiplet and SO(3) × U(1) × ℝ gauge group. The generalised structure associated with “BBBW” solutions yields two vector multiplets, one hypermultiplet and an abelian gauging. We argue that these are the most general consistent truncations on such backgrounds.

scholarly journals Invariant torsion and G2-metrics

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Diego Conti ◽  
Thomas Bruun Madsen
Keyword(s):  
Local Homogeneity ◽  
Spinor Bundle ◽  
Intrinsic Torsion

AbstractWe introduce and study a notion of invariant intrinsic torsion geometrywhich appears, for instance, in connection with the Bryant-Salamon metric on the spinor bundle over S3. This space is foliated by sixdimensional hypersurfaces, each of which carries a particular type of SO(3)-structure; the intrinsic torsion is invariant under SO(3). The last condition is sufficient to imply local homogeneity of such geometries, and this allows us to give a classification. We close the circle by showing that the Bryant-Salamon metric is the unique complete metric with holonomy G2 that arises from SO(3)-structures with invariant intrinsic torsion.

scholarly journals On certain classes of $$\mathbf{Sp}(4,\mathbb{R})$$ symmetric $$G_2$$ structures

2020 ◽  
Author(s):  
Paweł Nurowski
Keyword(s):  
Homogeneous Space ◽  
Lie Group ◽  
Real Form ◽  
Intrinsic Torsion

AbstractWe find two different families of $$\mathbf{Sp}(4,\mathbb{R})$$ Sp ( 4 , R ) symmetric $$G_2$$ G 2 structures in seven dimensions. These are $$G_2$$ G 2 structures with $$G_2$$ G 2 being the split real form of the simple exceptional complex Lie group $$G_2$$ G 2 . The first family has $$\tau _2\equiv 0$$ τ 2 ≡ 0 , while the second family has $$\tau _1\equiv \tau _2\equiv 0$$ τ 1 ≡ τ 2 ≡ 0 , where $$\tau _1$$ τ 1 , $$\tau _2$$ τ 2 are the celebrated $$G_2$$ G 2 -invariant parts of the intrinsic torsion of the $$G_2$$ G 2 structure. The families are different in the sense that the first one lives on a homogeneous space $$\mathbf{Sp}(4,\mathbb{R})/\mathbf{SL}(2,\mathbb{R})_l$$ Sp ( 4 , R ) / SL ( 2 , R ) l , and the second one lives on a homogeneous space $$\mathbf{Sp}(4,\mathbb{R})/\mathbf{SL}(2,\mathbb{R})_s$$ Sp ( 4 , R ) / SL ( 2 , R ) s . Here $$\mathbf{SL}(2,\mathbb{R})_l$$ SL ( 2 , R ) l is an $$\mathbf{SL}(2,\mathbb{R})$$ SL ( 2 , R ) corresponding to the $$\mathfrak{sl}(2,\mathbb{R})$$ sl ( 2 , R ) related to the long roots in the root diagram of $$\mathfrak{sp}(4,\mathbb{R})$$ sp ( 4 , R ) , and $$\mathbf{SL}(2,\mathbb{R})_s$$ SL ( 2 , R ) s is an $$\mathbf{SL}(2,\mathbb{R})$$ SL ( 2 , R ) corresponding to the $$\mathfrak{sl}(2,\mathbb{R})$$ sl ( 2 , R ) related to the short roots in the root diagram of $$\mathfrak{sp}(4,\mathbb{R})$$ sp ( 4 , R ) .

scholarly journals Superstrings with intrinsic torsion

2004 ◽  
Vol 69 (8) ◽  
Author(s):  
Jerome P. Gauntlett ◽  
Dario Martelli ◽  
Daniel Waldram
Keyword(s):  
Intrinsic Torsion

scholarly journals HARMONIC STRUCTURES AND INTRINSIC TORSION

2015 ◽  
Vol 20 (3) ◽  
pp. 699-723 ◽  
Author(s):  
DIEGO CONTI ◽  
THOMAS BRUUN MADSEN
Keyword(s):  
Intrinsic Torsion

scholarly journals Harmonic almost contact structures via the intrinsic torsion

2011 ◽  
Vol 181 (1) ◽  
pp. 145-187 ◽  
Author(s):  
J. C. González-Dávila ◽  
F. Martín Cabrera
Keyword(s):  
Contact Structures ◽  
Intrinsic Torsion

scholarly journals The intrinsic torsion of almost quaternion-Hermitian manifolds

2008 ◽  
Vol 58 (5) ◽  
pp. 1455-1497 ◽  
Author(s):  
Francisco Martín Cabrera ◽  
Andrew Swann
Keyword(s):  
Hermitian Manifolds ◽  
Intrinsic Torsion

REDUCED HOLONOMY, HYPERSURFACES AND EXTENSIONS

2006 ◽  
Vol 03 (05n06) ◽  
pp. 899-912 ◽  
Author(s):  
DIEGO CONTI ◽  
SIMON SALAMON
Keyword(s):  
Fundamental Form ◽  
General Problem ◽  
Holonomy Group ◽  
Second Fundamental Form ◽  
The Second Fundamental Form ◽  
Ricci Flat ◽  
Intrinsic Torsion

We study the geometry of hypersurfaces in manifolds with Ricci-flat holonomy group, on which we introduce a G-structure whose intrinsic torsion can be identified with the second fundamental form. The general problem of extending a manifold with such a G-structure so as to invert this construction is open, but results exist in particular cases, which we review. We list the five-dimensional nilmanifolds carrying invariant SU(2)-structures of this type, and present an example of an associated metric with holonomy SU(3).

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