Generalising Courant algebroids to M-theory

Arvanitakis, Alex S.

doi:10.22323/1.347.0127

Cited by 3 publications

(2 citation statements)

References 23 publications

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“…Courant algebroids were shown to have an L 3 -algebra in [49]. In the case of [52,53], where the correct L ∞ algebra was demonstrated to follow from interpreting the M theory geometries as dg-symplectic manifolds. More broadly speaking, the higher structures that feature in string and M theory are known to be classified by super homotopy theory, see the review [54] and references therein.…”

Section: M Theory Correctionsmentioning

confidence: 99%

Higher curvature Bianchi identities, generalized geometry, and L∞ algebras

Coimbra¹

2019

Phys. Rev. D

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The Bianchi identities for bosonic fluxes in supergravity can receive higher derivative quantum and string corrections, the most well known being that of Heterotic theory dH = 1 4 α (tr F 2 − tr R 2 ). Less studied are the modifications at order R 4 that may arise, for example, in the Bianchi identity for the seven-form flux of M theory compactifications. We argue that such corrections appear to be incompatible with the exceptional generalised geometry description of the lower order supergravity, and seem to imply a gauge algebra for the bosonic potentials that cannot be written in terms of an (exceptional) Courant bracket. However, we show that this algebra retains the form of an L ∞ gauge field theory, which terminates at a level ten multibracket.

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Section: M Theory Correctionsmentioning

confidence: 99%

Higher curvature Bianchi identities, generalized geometry, and L∞ algebras

Coimbra¹

2019

Phys. Rev. D

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“…For other branes, such as the M2 and M5 branes in M-theory, or even/odd D-branes in type II string theory, the corresponding algebroids are roughly speaking the ones that are classified by whichever fluxes couple electrically to the brane in question; such algebroids can be thought of as generalisations of Courant algebroids to e.g. M-theory scenarios, see [6] for this point of view, and [7] for an alternative.…”

Section: Introductionmentioning

confidence: 99%

Brane wrapping, AKSZ sigma models, and QP manifolds

Arvanitakis¹,

Tennyson²

2023

Preprint

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We introduce a technique to realise brane wrapping and double dimensional reduction in the context of AKSZ topological sigma models and also in their target spaces, which are symplectic L n -algebroids (i.e. QP-manifolds). Our procedure involves a novel coisotropic reduction combined with an AKSZ transgression that realises degree-shifting; the reduced QP-manifold depends on topological data of the 'wrapped' cycle. We check our procedure against the known rules for fluxes under wrapping in the context of M-theory/type IIA duality, and we also find a new relation between Courant algebroids and Poisson manifolds.

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