The Geometry, Branes and Applications of Exceptional Field Theory

Abstract

This is a review of exceptional field theory: a generalisation of Kaluza-Klein theory that unifies the metric and $p$-form gauge field degrees of freedom of supergravity into a generalised or extended geometry, whose additional coordinates may be viewed as conjugate to brane winding modes. This unifies the maximal supergravities, treating their previously-hidden exceptional Lie symmetries as a fundamental geometric symmetry. Duality orbits of solutions simplify into single objects, that in many cases have simple geometric interpretations, for instance as wave or monopole-type solutions. It also provides a route to explore exotic or non-geometric aspects of M-theory, such as exotic branes, U-folds, and more novel sorts of non-Riemannian spaces.

arXiv comment158 pages (including refs), invited review for International Journal of Modern Physics A, v2: refs added + typos fixed, v3: to match published version, v4: accumulated typo fixes

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• A note on Faddeev--Popov action for doubled-yet-gauged particle and graded Poisson geometry
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• Geometry of ${\mathbb{R}}^{+}\times E_{3(3)}$ Exceptional Field Theory and F-theory
• A note on T-folds and T3 fibrations
• Advantage of the second-order formalism in double space T-dualization of type II superstring
• Special Holonomy Manifolds, Domain Walls, Intersecting Branes and T-folds
• Reductions of Exceptional Field Theories
• Exotic Branes from del Pezzo Surfaces

Cited by in corpus (43)

• A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• A master exceptional field theory
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• Polyvector deformations in eleven-dimensional supergravity
• The generalized Bergshoeff-de Roo identification II
• Supersymmetry, T-duality and Heterotic ${\alpha }^{\prime }$-corrections
• Kaluza-Klein fermion mass matrices from Exceptional Field Theory and $\mathcal{N}=1$ spectra
• Non-abelian U-duality at work
• Supersymmetric spectroscopy on AdS${}_4\times S^7$ and AdS${}_4\times S^6$
• On non-abelian U-duality of 11D backgrounds
• A fresh view on string orbifolds
• Super-Chern-Simons spectra from Exceptional Field Theory
• Emergence of $R^4$-terms in M-theory
• Currents, charges and algebras in exceptional generalised geometry
• New N=1 AdS${}_4$ solutions of type IIB supergravity
• Maximal D=2 supergravities from higher dimensions
• Generalizing eleven-dimensional supergravity
• Generalized 11D supergravity equations from tri-vector deformations
• Vacua of $\omega$-deformed SO(8) supergravity
• Tri-vector deformations on compact isometries
• Five-brane Current Algebras in Type II String Theories
• Double Field Theory and Geometric Quantisation
• Infinite and finite consistent truncations on deformed generalised parallelisations
• Polyvector deformations of Type IIB backgrounds
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Integrability structures in string theory
• Exotic potentials and Bianchi identities in SL(5) exceptional field theory
• Generalised holonomies and K(E${}_9$)
• Canonical analysis of E${}_{6(6)}(\mathbb{R})$ invariant five dimensional (super-)gravity
• Open F-branes
• Consistent truncations from the geometry of sphere bundles
• World-volume Effective Theories of Locally Non-geometric Branes
• The puzzle of global Double Field Theory: open problems and the case for a Higher Kaluza-Klein perspective
• Non-isometric U-dualities
• The invariant action for solitonic 5-branes
• Black hole solutions in double field theory
• Double Field Theory and Pseudo-Supersymmetry
• The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces
• Localized Kaluza-Klein 6-brane
• $\mathcal{N}=1$ S-fold spectroscopy
• Generalised U-dual solutions in supergravity
• The canonical formulation of E${}_{6(6)}$ exceptional field theory