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 Generalised cosets

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Saskia Demulder ◽  
Falk Hassler ◽  
Giacomo Piccinini ◽  
Daniel C. Thompson
Keyword(s):  
Recent Work ◽  
Covariant Derivative ◽  
Tangent Bundle ◽  
Lie Symmetry ◽  
Lie Derivative ◽  
Spin Connection ◽  
Two Dimensional ◽  
Frame Field ◽  
Intrinsic Torsion ◽  
Consistent Truncations

Abstract Recent work has shown that two-dimensional non-linear σ-models on group manifolds with Poisson-Lie symmetry can be understood within generalised geometry as exemplars of generalised parallelisable spaces. Here we extend this idea to target spaces constructed as double cosets M = $$ \tilde{G} $$ G ˜ \𝔻/H. Mirroring conventional coset geometries, we show that on M one can construct a generalised frame field and a H -valued generalised spin connection that together furnish an algebra under the generalised Lie derivative. This results naturally in a generalised covariant derivative with a (covariantly) constant generalised intrinsic torsion, lending itself to the construction of consistent truncations of 10-dimensional supergravity compactified on M . An important feature is that M can admit distinguished points, around which the generalised tangent bundle should be augmented by localised vector multiplets. We illustrate these ideas with explicit examples of two-dimensional parafermionic theories and NS5-branes on a circle.

Note on Almost Product Manifolds and their Tangent Bundles

1966 ◽  
Vol 9 (05) ◽  
pp. 621-630
Author(s):  
Chorng Shi Houh
Keyword(s):  
Tangent Bundle ◽  
Tangent Vector ◽  
Product Structure ◽  
Dimensional Manifold ◽  
Almost Product Structure ◽  
Local Coordinates ◽  
Natural Frame ◽  
Class C ◽  
Tangent Bundles ◽  
Differentiability Class

Let Mn be an n-dimensional manifold of differentiability class C∞ with an almost product structure . Let have eigenvalue +1 of multiplicity p and eigenvalue -1 of multiplicity q where p+q = n and p≧1, q≧1. Let T(Mn) be the tangent bundle of M. T(Mn) is a 2n dimensional manifold of class C∞. Let xi be the local coordinates of a point P of Mn. The local coordinates of T(Mn) can be expressed by 2n variables (xi, yi) where xi are coordinates of the point P and yi are components of a tangent vector at P with respect to the natural frame constituted by the vectior ∂/∂xi at P.

When is an Anosov flow geodesic?

1992 ◽  
Vol 12 (2) ◽  
pp. 227-232
Author(s):  
Leon W. Green
Keyword(s):  
Flow Field ◽  
Tangent Bundle ◽  
Geodesic Flow ◽  
Vector Fields ◽  
Three Dimensional ◽  
Dimensional Manifold ◽  
Anosov Flow ◽  
Unit Tangent Bundle

AbstractLet X, H+, H− be vector fields tangent, respectively, to an Anosov flow and its expanding and contracting foliations in a compact three-dimensional manifold, with γ, α+, α− one forms dual to them. If α+([H+, H−]) = α−([H+, H−]) and γ([H+, H−]) = α−([X, H−]) − α+([X, H+]), then the manifold has the structure of the unit tangent bundle of a Riemannian orbifold with geodesic flow field X.

scholarly journals Complete lift of vector fields and sprays to T∞M

2015 ◽  
Vol 12 (10) ◽  
pp. 1550113 ◽  
Author(s):  
Ali Suri ◽  
Somaye Rastegarzadeh
Keyword(s):  
Vector Field ◽  
Differential Equations ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Dimensional Manifold ◽  
Closed Curves ◽  
Infinite Dimensional ◽  
Integral Curves ◽  
Complete Lift ◽  
Infinite Dimensional Manifold

In this paper for a given Banach, possibly infinite dimensional, manifold M we focus on the geometry of its iterated tangent bundle TrM, r ∈ ℕ ∪ {∞}. First we endow TrM with a canonical atlas using that of M. Then the concepts of vertical and complete lifts for functions and vector fields on TrM are defined which they will play a pivotal role in our next studies i.e. complete lift of (semi)sprays. Afterward we supply T∞M with a generalized Fréchet manifold structure and we will show that any vector field or (semi)spray on M, can be lifted to a vector field or (semi)spray on T∞M. Then, despite of the natural difficulties with non-Banach modeled manifolds, we will discuss about the ordinary differential equations on T∞M including integral curves, flows and geodesics. Finally, as an example, we apply our results to the infinite-dimensional case of manifold of closed curves.

scholarly journals Wrapped NS5-branes, consistent truncations and Inönü-Wigner contractions

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
K. C. Matthew Cheung ◽  
Rahim Leung
Keyword(s):  
Gauge Group ◽  
Discrete Group ◽  
Vector Multiplet ◽  
Consistent Truncations ◽  
Group Of Symmetries ◽  
Lower Dimensional ◽  
Kaluza Klein

Abstract We construct consistent Kaluza-Klein truncations of type IIA supergravity on (i) Σ2 × S3 and (ii) Σ3 × S3, where Σ2 = S2/Γ, ℝ2/Γ, or ℍ2/Γ, and Σ3 = S3/Γ, ℝ3/Γ, or ℍ3/Γ, with Γ a discrete group of symmetries, corresponding to NS5-branes wrapped on Σ2 and Σ3. The resulting theories are a D = 5, $$ \mathcal{N} $$ N = 4 gauged supergravity coupled to three vector multiplets with scalar manifold SO(1, 1) × SO(5, 3)/(SO(5) × SO(3)) and gauge group SO(2) × (SO(2) $$ {\ltimes}_{\Sigma_2} $$ ⋉ Σ 2 ℝ4) which depends on the curvature of Σ2, and a D = 4, $$ \mathcal{N} $$ N = 2 gauged supergravity coupled to one vector multiplet and two hypermultiplets with scalar manifold SU(1, 1)/U(1) × G2(2)/SO(4) and gauge group ℝ+ × ℝ+ for truncations (i) and (ii) respectively. Instead of carrying out the truncations at the 10-dimensional level, we show that they can be obtained directly by performing Inönü-Wigner contractions on the 5 and 4-dimensional gauged supergravity theories that come from consistent truncations of 11-dimensional supergravity associated with M5-branes wrapping Σ2 and Σ3. This suggests the existence of a broader class of lower-dimensional gauged supergravity theories related by group contractions that have a 10 or 11-dimensional origin.

SUB-WEYL GEOMETRY AND ITS LINEAR CONNECTIONS

2012 ◽  
Vol 09 (05) ◽  
pp. 1250047 ◽  
Author(s):  
OANA CONSTANTINESCU ◽  
MIRCEA CRASMAREANU
Keyword(s):  
Tangent Bundle ◽  
Natural Extension ◽  
Conformal Structure ◽  
Point Of View ◽  
Dimensional Manifold ◽  
Finsler Spaces ◽  
Weyl Geometry ◽  
Cartan Form ◽  
Linear Connections ◽  
Local Expression

The aim of this paper is to study from the point of view of linear connections the data [Formula: see text] with M a smooth (n+p)-dimensional real manifold, [Formula: see text] an n-dimensional manifold semi-Riemannian distribution on M, [Formula: see text] the conformal structure generated by g and W a Weyl substructure: a map [Formula: see text] such that W(ḡ) = W(g) - du, ḡ = eug;u ∈ C∞(M). Compatible linear connections are introduced as a natural extension of similar notions from Weyl geometry and such a connection is unique if a symmetry condition is imposed. In the foliated case the local expression of this unique connection is obtained. The notion of Vranceanu connection is introduced for a pair (Weyl structure, distribution) and it is computed for the tangent bundle of Finsler spaces, particularly Riemannian, choosing as distribution the vertical bundle of tangent bundle projection and as one-form the Cartan form.

scholarly journals SEMISTABILITY OF RESTRICTED TANGENT BUNDLES AND A QUESTION OF I. BISWAS

2013 ◽  
Vol 24 (01) ◽  
pp. 1250122 ◽  
Author(s):  
PRISKA JAHNKE ◽  
IVO RADLOFF
Keyword(s):  
Riemann Surface ◽  
Abelian Variety ◽  
Tangent Bundle ◽  
Compact Riemann Surface ◽  
Projective Manifold ◽  
Holomorphic Map ◽  
Complex Projective ◽  
Tangent Bundles

Let M be a complex projective manifold with the property that for any compact Riemann surface C and holomorphic map f : C → M the pullback of the tangent bundle of M is semistable. We prove that in this case M is a curve or a finite étale quotient of an abelian variety answering a conjecture of Biswas.

CANONICAL FORM IN SECOND-ORDER FRAME BUNDLES IN A NATURAL WAY

2014 ◽  
Vol 25 (01) ◽  
pp. 1450009 ◽  
Author(s):  
A. MARTÍN MÉNDEZ
Keyword(s):  
Canonical Form ◽  
Tangent Bundle ◽  
Principal Bundle ◽  
Second Order ◽  
Natural Projection ◽  
Dimensional Manifold ◽  
Frame Bundle ◽  
Natural Way ◽  
Bundle Structure

Using horizontal n-bases of the tangent bundle of the linear frame bundle [Formula: see text] of an n-dimensional manifold M, the canonical form in the non-holonomic second-order frame bundle of M is introduced as a restriction of the canonical form of the bundle [Formula: see text]. This construction generalizes the ones in the corresponding semi-holonomic and holonomic second-order frame bundles. We prove that the natural projection of the set of all non-holonomic second-order frames of M into [Formula: see text] defines a principal bundle structure.

HOMOTOPY DECOMPOSITIONS OF GAUGE GROUPS OVER RIEMANN SURFACES AND APPLICATIONS TO MODULI SPACES

2011 ◽  
Vol 22 (12) ◽  
pp. 1711-1719 ◽  
Author(s):  
STEPHEN D. THERIAULT
Keyword(s):  
Riemann Surface ◽  
Gauge Group ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Riemann Surfaces ◽  
Vector Bundles ◽  
Homotopy Groups ◽  
Gauge Groups ◽  
Stable Vector Bundles

For a prime p, the gauge group of a principal U(p)-bundle over a compact, orientable Riemann surface is decomposed up to homotopy as a product of spaces, each of which is commonly known. This is used to deduce explicit computations of the homotopy groups of the moduli space of stable vector bundles through a range, answering a question of Daskalopoulos and Uhlenbeck.

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