Twisted Cohomotopy Implies M-Theory Anomaly Cancellation on 8-Manifolds

Fiorenza, Domenico; Sati, Hisham; Schreiber, Urs

doi:10.1007/s00220-020-03707-2

Cited by 42 publications

(45 citation statements)

References 123 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We prove that the topological charge structure of fundamental super M‐branes produces twisted K‐theory charges of Type IIA D‐branes under double dimensional reduction when all torsion effects are ignored. Our result is based upon Sati's conjecture that the topological M‐brane charge is classified by degree‐4 cohomotopy, and our result in turn contributes to a growing body of evidence for this conjecture (see []).…”

supporting

confidence: 54%

Parametrised Homotopy Theory and Gauge Enhancement

Braunack-Mayer

2019

Fortschritte der Physik

View full text Add to dashboard Cite

show abstract

supporting

confidence: 54%

Parametrised Homotopy Theory and Gauge Enhancement

Braunack-Mayer

2019

Fortschritte der Physik

View full text Add to dashboard Cite

show abstract

“…It sounds reasonable to use our Higher Kaluza‐Klein geometry to formalize ExFT (see [61]). Let us consider the M2‐M5‐brane gerbe from [42] over the 11 d spacetime manifold M . This will be encoded by a particular Čech cocycle, which includes a collection of 2‐forms

Λ_{α β}^{normalM 2}

and 5‐forms

Λ_{α β}^{normalM 5}

on two‐fold overlaps of patches

U_{α} \cap U_{β}

.…”

Section: Discussionmentioning

confidence: 99%

“…Higher geometry is being also successfully applied to the fundamental understanding of M‐theory by [40], [42], [47], [48], [19] and [65]. In these references the topological and differential structure of M‐theory is investigated, until remarkably a proposal for the generalized cohomology theory that charge‐quantizes the supergravity C ‐field is made ( Hypothesis H ) by [50]. This idea was further explored by [27], [113] and [49].…”

Section: Introductionmentioning

confidence: 99%

Global Double Field Theory is Higher Kaluza‐Klein Theory

Alfonsi

2020

Fortschritte der Physik

View full text Add to dashboard Cite

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.

show abstract

“…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. In particular, note that the Heterotic generalised geometry that we described earlier corresponds to a "string Lie 2-algebra" [55], while anomaly cancelation in M theory was examined in this formalism in [56].…”

Section: M Theory Correctionsmentioning

confidence: 99%

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

Coimbra¹

2019

Phys. Rev. D

View full text Add to dashboard Cite

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.

show abstract

Twisted Cohomotopy Implies M-Theory Anomaly Cancellation on 8-Manifolds

Cited by 42 publications

References 123 publications

Parametrised Homotopy Theory and Gauge Enhancement

Parametrised Homotopy Theory and Gauge Enhancement

Global Double Field Theory is Higher Kaluza‐Klein Theory

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

Contact Info

Product

Resources

About