Double field theory and geometric quantisation

Alfonsi, Luigi; Berman, David S.

doi:10.1007/jhep06(2021)059

Cited by 6 publications

(3 citation statements)

References 71 publications

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“…Much of the machinery in place in this paper is insensitive to this concern, and it seems likely that a quantum mechanical approach would be required to progress. It would be interesting to combine the ideas in this paper with the technique of geometric quantisation as has been considered in the Abelian case [50].…”

Section: Discussionmentioning

confidence: 99%

A QP perspective on topology change in Poisson–Lie T-duality

Arvanitakis

Blair

Thompson

2023

J. Phys. A: Math. Theor.

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We describe topological T-duality and Poisson-Lie T-duality in terms of QP (differential graded symplectic) manifolds and their canonical transformations. Duality is mediated by a QP-manifold on doubled non-abelian ``correspondence'' space, from which we can perform mutually dual symplectic reductions, where certain canonical transformations play a vital role. In the presence of spectator coordinates, we show how the introduction of a bibundle structure on correspondence space realises changes in the global fibration structure under Poisson-Lie duality. Our approach can be directly translated to the worldsheet to derive dual string current algebras. Finally, the canonical transformations appearing in our reduction procedure naturally suggest a Fourier-Mukai integral transformation for Poisson-Lie T-duality.

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Section: Discussionmentioning

confidence: 99%

A QP perspective on topology change in Poisson–Lie T-duality

Arvanitakis

Blair

Thompson

2023

J. Phys. A: Math. Theor.

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“…Some loop calculations in ExFT have already been carried out in [8,9] for special geometries. Double field theory has recently been discussed in the context of geometric quantisation in [10] and the extension of the results to ExFT has also been commented on.…”

Section: Jhep07(2021)145mentioning

confidence: 99%

“…Finally the canonical formulation of exceptional field theory may be seen as the starting point for the canonical quantisation procedure. Some loop calculations in exceptional field theory -for special geometries that are of the form of Minkowski space times a compact torus -have already been carried out in [8,9] and the geometric quantisation of exceptional field theory has recently been commented on in [10].…”

Section: Introductionmentioning

confidence: 99%

The canonical formulation of E6(6) exceptional field theory

Kreutzer

2021

J. High Energ. Phys.

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We investigate the canonical formulation of the (bosonic) E6(6) exceptional field theory. The explicit non-integral (not manifestly gauge invariant) topological term of E6(6) exceptional field theory is constructed and we consider the canonical formulation of a model theory based on the topological two-form kinetic term. Furthermore we construct the canonical momenta and the canonical Hamiltonian of the full bosonic E6(6) exceptional field theory. Most of the canonical gauge transformations and some parts of the canonical constraint algebra are calculated. Moreover we discuss how to translate the results canonically into the generalised vielbein formulation. We comment on the possible existence of generalised Ashtekar variables.

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Noncommutative double geometry

Kodžoman,

Lescano

2024

Phys. Rev. D

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We construct noncommutative theories with the Moyal-Weyl product in the double field theory (DFT) framework. We deform the infinitesimal generalized diffeomorphisms and the Leibniz rule in a consistent way. The prescription requires a generalized star metric, which can be thought of as the fundamental double metric, in order to construct the action. Finally we use the generalized scalar field dynamics and the generalized scalar field-perfect fluid correspondence to construct the generalized energy-momentum tensor of a perfect fluid in the noncommutative double geometry. The present formalism paves the way to the study of string cosmologies scenarios including the Moyal-Weyl product in a T-duality invariant way. Published by the American Physical Society 2024

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Double field theory and geometric quantisation

Cited by 6 publications

References 71 publications

A QP perspective on topology change in Poisson–Lie T-duality

A QP perspective on topology change in Poisson–Lie T-duality

The canonical formulation of E6(6) exceptional field theory

Noncommutative double geometry

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