Timelike duality, M′-theory and an exotic form of the Englert solution

Henneaux, Marc; Ranjbar, Arash

doi:10.1007/jhep08(2017)012

Cited by 5 publications

(24 citation statements)

References 28 publications

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“…As our last comment we point out that an application of this result as a way to construct Englert-type solutions of exotic M -theory has been discussed in [19] where S 3,4 = Spin (3,4) G 2,2 appears as the internal manifold in dimensional reduction of exotic supergravity in 6 + 5 dimensions (low energy limit of M -theory).…”

Section: Extensionsmentioning

confidence: 86%

“…Extending the proof to the pseudo-Riemannian case, we saw that a similar construction is possible for H 4,3 = SO(4, 3)/G 2,2 with torsion proportional tof a bc , which is invariant under G 2,2 ⊂ SO (4,3). In this case, torsion breaks the SO(4, 4) symmetry of round seven-pseudo-sphere (or seven-pseudo-hyperbolic space) down to SO(4, 3) [19]. This can also be seen geometrically using the isomorphism between the imaginary split octonion vector space and the tangent space on H 4,3 .…”

Section: Extensionsmentioning

confidence: 88%

“…As discussed in [16,17], a similar role is also played by H 4,3 = SO(4, 4)/SO(4, 3) (or rather by S 3,4 = SO(4, 4)/SO (3,4)) as an internal manifold in the compactification of timelike T-dual M-theory (more precisely the supergravity theory at low energy limit of M -theory) [18], where one obtains an AdS 4 maximal supergravity with a local SO (4,4) symmetry. An extension of this analysis in [19] showed that the squashed H 4,3 = SO(4, 3)/G 2,2 can be realized as an internal manifold in the dimensional reduction of M -theory. In that case, the resulting 4-dimensional supergravity is a nonsupersymmetric theory.…”

Section: Introductionmentioning

confidence: 96%

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Flat $\mathfrak{so}(\,p,q)$ -connections for manifolds of non-Euclidean signature

Ranjbar

Zanelli

2019

Class. Quantum Grav.

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The well-known fact that S 1 , S 3 and S 7 are parallelizable manifolds admitting flat connections is revisited. The role of torsion in the construction of those flat connections is made explicit, and the possibilities allowed by different metric signatures are examined. A necessary condition for parallelizability in an open region is that the torsion tensor must be covariantly constant. This property can be used to obtain a relation between a torsion-free and flat connections. Our treatment covers Riemannian and pseudo-Riemannian (non-Euclidean signature) hyperbolic manifolds of dimensions three and seven. Apart from the spherical cases mentioned above, the explicit flat so(p, q) connections with p + q = 3, 7 and p − q = 1 are constructed for the coset manifolds SO(p, q + 1)/SO(p, q).

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Section: Extensionsmentioning

confidence: 86%

Section: Extensionsmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 96%

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Flat $\mathfrak{so}(\,p,q)$ -connections for manifolds of non-Euclidean signature

Ranjbar

Zanelli

2019

Class. Quantum Grav.

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“…We will show that the compactification on parallelizable S 3,4 is possible if one works in the picture described by one of these dual theories, known as M -theory [1]. This solution, similarly to the Englert solution, will result in a non-supersymmetric theory in AdS 4 background.…”

Section: Introductionmentioning

confidence: 90%

Conformal field theories from deformations of theories with $W_n$ symmetry

Babaro,

Giribet,

Ranjbar

2016

Preprint

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This thesis is devoted to various questions connected with duality. It is composed of two parts.The first part discusses some aspects of timelike T-duality. We explore the possibility of compactification of supergravity theories with various signatures (low energy limit of M -theories which are dual under timelike T-dualities) on parallelizable internal seven dimensional (pseudo-)spheres. We show that, beside the standard theory, only one of the dual theories known as M -theory can admit such a solution. The effective four dimensional theory is non-supersymmetric and due to the presence of torsion the symmetry of seven dimensional (pseudo-)sphere breaks down to Spin(3, 4).In the second part, in an attempt to have a systematic discussion of gaugings in supergravity, we show the isomorphism between the space of local deformations of the appropriate zero coupling limit of the embedding tensor Lagrangian and that of the second-order scalar-vector Lagrangian, describing the bosonic sector of supergravity ignoring gravity, in a chosen duality frame determined by embedding tensors. We analyze the BV-BRST deformation of a class of scalar-vector coupled Lagrangians, which contains supergravity Lagrangians as examples, and find a set of constraints that guarantee the consistency of the deformations of the Lagrangians. We show in principle that for a large class of theories considered in this thesis, the only deformations are those of the Yang-Mills type associated with a subgroup of the rigid symmetries.

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“…10 This can be made more explicit by comparing ϕ (2) with ϕ (1) for χ 2 = aχ 1 + ib μ γ μ χ 1 . 11 See also [40].…”

mentioning

confidence: 99%

Supersymmeric Gauge Theory on Curved 7‐Branes

Prins

2019

Fortschritte der Physik

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We construct novel 7d supersymmetric gauge theories which include a Chern‐Simons‐like term on curved spaces. In order to so, we examine the supersymmetry constraints for E7‐branes in type IIA* theory, rather than making use of an off‐shell supergravity. We find two classes of solutions to the constraints, expressed in terms of a G2‐structure with non‐vanishing intrinsic torsion. The supersymmetric gauge theories are then obtained by coupling flat gauge theory to such supersymmetric backgrounds. Various examples are given, including round and squashed S7 as well as S3×M4 with M4 hyperkähler.

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Timelike duality, M′-theory and an exotic form of the Englert solution

Cited by 5 publications

References 28 publications

Flat $\mathfrak{so}(\,p,q)$ -connections for manifolds of non-Euclidean signature

Flat $\mathfrak{so}(\,p,q)$ -connections for manifolds of non-Euclidean signature

Conformal field theories from deformations of theories with $W_n$ symmetry

Supersymmeric Gauge Theory on Curved 7‐Branes

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