A Kaluza–Klein Approach to Double and Exceptional Field Theory

Berman, David S.

doi:10.1002/prop.201910002

Cited by 17 publications

(20 citation statements)

References 74 publications

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“…Exceptional field theory is the extension of double field theory to M-theory where the U-duality group becomes a manifest symmetry. See [75,76] for a recent reviews. Usually the properties of double field theory are shared with exceptional field theory.…”

Section: Jhep06(2021)059 7 Discussionmentioning

confidence: 99%

Double field theory and geometric quantisation

Alfonsi

Berman

2021

J. High Energ. Phys.

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We examine various properties of double field theory and the doubled string sigma model in the context of geometric quantisation. In particular we look at T-duality as the symplectic transformation related to an alternative choice of polarisation in the construction of the quantum bundle for the string. Following this perspective we adopt a variety of techniques from geometric quantisation to study the doubled space. One application is the construction of the “double coherent state” that provides the shortest distance in any duality frame and a “stringy deformed” Fourier transform.

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Section: Jhep06(2021)059 7 Discussionmentioning

confidence: 99%

Double field theory and geometric quantisation

Alfonsi

Berman

2021

J. High Energ. Phys.

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“…This has been extended in various ways, first in [73] and then more recently in [74,75] where the NS two form of supergravity was included in the ansatz. The insight in [74,75] was to use the Double Field Theory [76][77][78][79] description of supergravity, see [80][81][82][83] and references therein for a review. Double Field Theory combines the metric and two-form into a single object called "the generalised metric" .…”

Section: Jhep04(2021)071mentioning

confidence: 99%

The classical double copy for M-theory from a Kerr-Schild ansatz for exceptional field theory

Berman

Kim

Lee

2021

J. High Energ. Phys.

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We construct the classical double copy formalism for M-theory. This extends the current state of the art by including the three form potential of eleven dimensional supergravity along with the metric. The key for this extension is to construct a Kerr-Schild type Ansatz for exceptional field theory. This Kerr-Schild Ansatz then allows us to find the solutions of charged objects such as the membrane from a set of single copy fields. The exceptional field theory formalism then automatically produces the IIB Kerr-Schild ansatz allowing the construction of the single copy for the fields of IIB supergravity (with manifest SL(2) symmetry).

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“…The resulting generalized metric is a (locally defined) version of Higher Kaluza‐Klein monopole on this particular background. In [9] it is argued that, in the case of an torus compactified spacetime we can write Higher Dirac monopole in terms of an ordinary Dirac monopole by

H^{3} false(S^{2} \times S^{1}, double-struckZ false) ≅ H^{2} false(S^{2}, double-struckZ false) \otimes_{double-struckZ} H^{1} false(S^{1}, double-struckZ false)

. But also that a full DFT monopole should require a geometrization of the gerbe which is impossible to achieve with just manifolds: Higher Kaluza‐Klein geometry is hopefully an answer to this.…”

Section: Application: Ns5‐brane Is Higher Kaluza‐klein Monopolementioning

confidence: 99%

Global Double Field Theory is Higher Kaluza‐Klein Theory

Alfonsi

2020

Fortschritte der Physik

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Kaluza-Klein Theory states that a metric on the total space of a principal bundle P → M, if it is invariant under the principal action of P, naturally reduces to a metric together with a gauge field on the base manifold M. We propose a generalization of this Kaluza-Klein principle to higher principal bundles and higher gauge fields. For the particular case of the abelian gerbe of Kalb-Ramond field, this Higher Kaluza-Klein geometry provides a natural global formulation for Double Field Theory (DFT). In this framework the doubled space is the total space of a higher principal bundle and the invariance under its higher principal action is exactly a global formulation of the familiar strong constraint. The patching problem of DFT is naturally solved by gluing the doubled space with a higher group of symmetries in a higher category. Locally we recover the familiar picture of an ordinary para-Hermitian manifold equipped with Born geometry. Infinitesimally we recover the familiar picture of a higher Courant algebroid twisted by a gerbe (also known as Extended Riemannian Geometry). As first application we show that on a torus-compactified spacetime the Higher Kaluza-Klein reduction gives automatically rise to abelian T-duality, while on a general principal bundle it gives rise to non-abelian T-duality. As final application we define a natural notion of Higher Kaluza-Klein monopole by directly generalizing the ordinary Gross-Perry one. Then we show that under Higher Kaluza-Klein reduction, this monopole is exactly the NS5-brane on a 10d spacetime. If, instead, we smear it along a compactified direction we recover the usual DFT monopole on a 9d spacetime.

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A Kaluza–Klein Approach to Double and Exceptional Field Theory

Cited by 17 publications

References 74 publications

Double field theory and geometric quantisation

Double field theory and geometric quantisation

The classical double copy for M-theory from a Kerr-Schild ansatz for exceptional field theory

Global Double Field Theory is Higher Kaluza‐Klein Theory

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