Conformal Courant Algebroids and Orientifold T-Duality

Baraglia, David

doi:10.1142/s0219887812500843

Cited by 15 publications

(13 citation statements)

References 39 publications

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“…(The same argument can be seen in [Bar13].) • Let ι : Π → Π denote the homeomorphism ι(k x , k y ) = (k x , k y + 1/2).…”

Section: T-duality Between Atiyah-hirzebruch Spectral Sequencesmentioning

confidence: 95%

Twisted crystallograpic T-duality via the Baum--Connes isomorphism

Gomi,

Kubota,

Thiang

2021

Preprint

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“…(The same argument can be seen in [Bar13].) • Let ι : Π → Π denote the homeomorphism ι(k x , k y ) = (k x , k y + 1/2).…”

Section: T-duality Between Atiyah-hirzebruch Spectral Sequencesmentioning

confidence: 95%

Twisted crystallograpic T-duality via the Baum--Connes isomorphism

Gomi,

Kubota,

Thiang

2021

Preprint

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“…The key point relevant to the O-fold construction is that we should require the Y-tensor be preserved by whatever we are quotienting by, so that generalised diffeomorphisms are preserved as a symmetry of ExFT. This will of course be guaranteed if we only take quotients with respect to subgroups of E d(d) , but note that for O(d, d) [1,24], the Z 2 quotient leading to orientifolds is not an element of O(d, d), but does leave Y MN KL invariant. The coordinate dependence on the extended coordinates Y M is constrained by the section condition:…”

Section: Pos(corfu2018)137mentioning

confidence: 99%

Orbifolds and Orientifolds as O-folds

Blair¹

2019

Proceedings of Corfu Summer Institute 2018 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2018)

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We consider quotients of string and M-theory by discrete subgroups of the U-duality group. This results in what we call O-folds, which are generalisations of orbifolds and orientifolds, and generically involve non-geometric identifications between physical coordinates and dual winding coordinates. A simple Z 2 quotient encodes the half-maximal duality web, describing on the same footing the Hořava-Witten description of M-theory on an interval, the heterotic theories, and type II in the presence of orientifold planes. This can be analysed using exceptional field theory, including the introduction of extra vector multiplets at the fixed points. This is an overview of the paper [1], based on a talk given at the Corfu Summer Institute 2018.

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“…Local double field theory geometrizes the Kalb-Ramond B-field and T -duality, whereas exceptional field theories do the same thing for other sectors and U -duality by making use of different algebroids [4]. There are many other algebroid structures such as metric algebroids [5], dull alberoids [6], conformal Courant algebroids [7] that are used in the string or M theory literature. All of these are special cases for local pre-Leibniz algebroids as the latter is defined by using just a few axioms.…”

Section: Introductionmentioning

confidence: 99%

“…Similarly, these proofs depend on the admissibility of the connection. In Section (7), we finish the paper with some concluding remarks.…”

Section: Introductionmentioning

confidence: 99%

Statistical Geometry and Hessian Structures on Pre-Leibniz Algebroids

Doğan

2021

Preprint

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We introduce statistical, conjugate connection and Hessian structures on anti-commutable pre-Leibniz algebroids. Anti-commutable pre-Leibniz algebroids are special cases of local pre-Leibniz algebroids, which are still general enough to include many physically motivated algebroids such as Lie, Courant, metric and higher-Courant algebroids. They create a natural framework for generalizations of differential geometric structures on a smooth manifold. The symmetrization of the bracket on an anti-commutable pre-Leibniz algebroid satisfies a certain property depending on a choice of an equivalence class of connections which are called admissible. These admissible connections are shown to be necessary to generalize aforementioned structures on pre-Leibniz algebroids. Consequently, we prove that, provided certain conditions, statistical and conjugate connection structures are equivalent when defined for admissible connections. Moreover, we also show that for 'projected-torsion-free' connections, one can generalize Hessian metrics and Hessian structures. We prove that any Hessian structure yields a statistical structure, where these results are completely parallel to the ones in the manifold setting. We also prove a mild generalization of the fundamental theorem of statistical geometry. Moreover, we generalize α-connections, strongly conjugate connections and relative torsion operator, and prove some analogous results.

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Conformal Courant Algebroids and Orientifold T-Duality

Cited by 15 publications

References 39 publications

Twisted crystallograpic T-duality via the Baum--Connes isomorphism

Twisted crystallograpic T-duality via the Baum--Connes isomorphism

Orbifolds and Orientifolds as O-folds

Statistical Geometry and Hessian Structures on Pre-Leibniz Algebroids

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