An Action for F-theory: $\mathrm{SL}(2)\times {\mathbb{R}}^{+}$ Exceptional Field Theory

Abstract

We construct the 12-dimensional exceptional field theory associated to the group $\mathrm{SL}(2)\times {\mathbb{R}}^{+}$ . Demanding the closure of the algebra of local symmetries leads to a constraint, known as the section condition, that must be imposed on all fields. This constraint has two inequivalent solutions, one giving rise to 11-dimensional supergravity and the other leading to F-theory. Thus $\mathrm{SL}(2)\times {\mathbb{R}}^{+}$ exceptional field theory contains both F-theory and M-theory in a single 12-dimensional formalism.

50 pages, plain Latex; v2 references updated and minor typos fixed

References in corpus (18)

• Double Field Theory
• Generalized Geometry and M theory
• Exceptional Field Theory III: E${}_{8(8)}$
• Gauged Double Field Theory
• Double Field Theory Formulation of Heterotic Strings
• Generalized E(7(7)) coset dynamics and D=11 supergravity
• Supersymmetric E${}_{7(7)}$ Exceptional Field Theory
• Exceptional field theory: $SO(5,5)$
• Tensor Hierarchy and Generalized Cartan Calculus in SL(3)$\times$SL(2) Exceptional Field Theory
• Finite Gauge Transformations and Geometry in Double Field Theory
• Fermions and Supersymmetry in ${\mathrm{E}}_{6(6)}$ Exceptional Field Theory
• Strings and Branes are Waves
• Type IIB flux vacua from G-theory II
• Type IIB flux vacua from G-theory I
• Exceptional geometry and tensor fields
• A note on large gauge transformations in double field theory
• Gaugings from E7 Extended Geometries
• F-theory with zeroth-quantized ghosts

Cited by in corpus (45)

• Half-maximal supersymmetry from exceptional field theory
• Generalized gravity from modified DFT
• The Geometry, Branes and Applications of Exceptional Field Theory
• Generalized IIB supergravity from exceptional field theory
• Beyond E11
• Non-Riemannian geometry of M-theory
• A master exceptional field theory
• On supersymmetric E11 exceptional field theory
• E${}_9$ exceptional field theory II. The complete dynamics
• 7-dimensional $\mathcal{N}=2$ Consistent Truncations using $\mathrm{SL}(5)$ Exceptional Field Theory
• Weaving the Exotic Web
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• The Exceptional Sigma Model
• Leibniz Gauge Theories and Infinity Structures
• Leibniz-Chern-Simons Theory and Phases of Exceptional Field Theory
• Effective Action for Non-Geometric Fluxes from Duality Covariant Actions
• Exotic branes in Exceptional Field Theory: the SL(5) duality group
• From Exceptional Field Theory to Heterotic Double Field Theory via K3
• Exotic Branes in Exceptional Field Theory: $E_{7(7)}$ and Beyond
• Generalized Parallelizable Spaces from Exceptional Field Theory
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• Exceptional M-brane sigma models and $\eta$-symbols
• Doubled strings, negative strings and null waves
• Particle actions and brane tensions from double and exceptional geometry
• Infinity-enhancing of Leibniz algebras
• Type II strings are Exceptional
• Open exceptional strings and D-branes
• O-folds: Orientifolds and Orbifolds in Exceptional Field Theory
• Maximal D=2 supergravities from higher dimensions
• New N=1 AdS${}_4$ solutions of type IIB supergravity
• A Kaluza-Klein Approach to Double and Exceptional Field Theory
• A geometric formulation of exceptional field theory
• Exceptional field theories, superparticles in an enlarged 11D superspace and higher spin theories
• Extended geometry of magical supergravities
• Uplifts of maximal supergravities and transitions to non-geometric vacua
• Geometry of ${\mathbb{R}}^{+}\times E_{3(3)}$ Exceptional Field Theory and F-theory
• Gauge field corrections to 11-dimensional supergravity via dimensional reduction
• Reductions of Exceptional Field Theories
• On effective field theory of F-theory beyond leading order
• Duality Covariant Solutions in Extended Field Theories
• The many facets of exceptional field theory
• Localized Kaluza-Klein 6-brane
• Exotic Aspects of Extended Field Theories
• The canonical formulation of E${}_{6(6)}$ exceptional field theory
• Toroidal $\&$ orbifold compactifications at large D and D-duality