Double Field Theory and Geometric Quantisation

Alfonsi, Luigi; Berman, David S.

doi:10.48550/arxiv.2101.12155

Cited by 3 publications

(4 citation statements)

References 61 publications

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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: Discussionmentioning

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%

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The canonical formulation of E$_{6(6)}$ exceptional field theory

Kreutzer

2021

Preprint

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We investigate the canonical formulation of the (bosonic) E 6(6) exceptional field theory. The explicit non-integral (not manifestly gauge invariant) topological term of E 6(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 E 6(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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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The canonical formulation of E$_{6(6)}$ exceptional field theory

Kreutzer

2021

Preprint

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“…Moreover, since the non-perturbative quantisation of strings and branes can be achieved by higher geometric quantisation [SS11, BSS17, BS17, FRS16], the close relation we established between extended and higher geometries will have a profound impact on the problem of quantisation. This issue, among other ones, was started to be studied in [AB21].…”

Section: Discussionmentioning

confidence: 99%

Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory

Alfonsi

2021

Preprint

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In this short paper, we will review the proposal of a correspondence between the doubled geometry of Double Field Theory and the higher geometry of bundle gerbes. Double Field Theory is T-duality covariant formulation of the supergravity limit of String Theory, which generalises Kaluza-Klein theory by unifying metric and Kalb-Ramond field on a doubled-dimensional space. In light of the proposed correspondence, this doubled geometry is interpreted as an atlas description of the higher geometry of bundle gerbes. In this sense, Double Field Theory can be interpreted as a field theory living on the total space of the bundle gerbe, just like Kaluza-Klein theory is set on the total space of a principal bundle. This correspondence provides a higher geometric interpretation for para-Hermitian geometry which opens the door to its generalisation to the other Extended Field Theories. This review is based on, but not limited to, my talk at the workshop Generalized Geometry and Applications at Universität Hamburg on 3rd of March 2020.

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“…Tools of conventional classical field theory, like Legendre transformations or canonical transformations, have to be reconsidered. Generalising techniques of geometric quantisation from the recently studies O(d, d) case[85] could be necessary, as well.…”

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confidence: 99%

Currents, charges and algebras in exceptional generalised geometry

Osten

2021

Preprint

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A classical E d(d) -invariant Hamiltonian formulation of world-volume theories of half-BPS p-branes in type IIb and eleven-dimensional supergravity is proposed, extending known results to d ≤ 6. It consists of a Hamiltonian, characterised by a generalised metric, and a current algebra constructed s.t. it reproduces the E d(d) generalised Lie derivative. E d(d) -covariance necessitates the introduction of so-called charges, specifying the type of p-brane and the choice of section. For p > 2, currents of p-branes are generically non-geometric due to the imposition of U-duality, e.g. the M5-currents contain coordinates associated to the M2-momentum.A derivation of the E d(d) -invariant current algebra from a canonical Poisson structure is in general not possible. At most, one can derive a current algebra associated to para-Hermitian exceptional geometry.The membrane in the SL(5)-theory is studied in detail. It is shown that in a generalised frame the current algebra is twisted by the generalised fluxes. As a consistency check, the double dimensional reduction from membranes in M-theory to strings in type IIa string theory is performed. Many features generalise to p-branes in SL(p + 3) generalised geometries that form building blocks for the E d(d) -invariant currents.

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Double Field Theory and Geometric Quantisation

Cited by 3 publications

References 61 publications

The canonical formulation of E$_{6(6)}$ exceptional field theory

The canonical formulation of E$_{6(6)}$ exceptional field theory

Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory

Currents, charges and algebras in exceptional generalised geometry

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