Geometry of ${\mathbb{R}}^{+}\times E_{3(3)}$ Exceptional Field Theory and F-theory

Abstract

We consider a non trivial solution to the section condition in the context of ${\mathbb{R}}^{+}\times E_{3(3)}$ exceptional field theory and show that allowing fields to depend on the additional stringy coordinates of the extended internal space permits to describe the monodromies of (p,q) 7-branes in the context of F-theory. General expressions of non trivial fluxes with associated linear and quadratic constraints are obtained via a comparison to the embedding tensor of eight dimensional gauged maximal supergravity with gauged trombone symmetry. We write an explicit generalised Christoffel symbol for $E_{3(3)}$ EFT and show that the equations of motion of F-theory, namely the vanishing of a 4 dimensional Ricci tensor with two of its dimensions fibered, can be obtained from a generalised Ricci tensor and an appropriate type IIB ansatz for the metric.

References in corpus (51)

• Unity of Superstring Dualities
• Evidence for F-Theory
• Double Field Theory
• Generalized metric formulation of double field theory
• A Geometry for Non-Geometric String Backgrounds
• Background independent action for double field theory
• Generalised Geometry for M-Theory
• Doubled Geometry and T-Folds
• The gauge algebra of double field theory and Courant brackets
• On Lagrangians and Gaugings of Maximal Supergravities
• Generalized Geometry and M theory
• Supergravity as Generalised Geometry I: Type II Theories
• M-theory, exceptional generalised geometry and superpotentials
• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• Lectures on F-theory compactifications and model building
• A field-theory motivated approach to symbolic computer algebra
• Exceptional Field Theory III: E${}_{8(8)}$
• The gauge structure of generalised diffeomorphisms
• NS5-Branes, T-Duality and Worldsheet Instantons
• Lectures on Gauged Supergravity and Flux Compactifications
• Double Field Theory of Type II Strings
• Exceptional Field Theory II: E${}_{7(7)}$
• Generalised T-Duality and Non-Geometric Backgrounds
• Duality Invariant Actions and Generalised Geometry
• Unification of Type II Strings and T-duality
• The local symmetries of M-theory and their formulation in generalised geometry
• Extended geometry and gauged maximal supergravity
• Exotic Branes in String Theory
• Exceptional field theory: $SL(5)$
• Worldsheet Instanton Corrections to the Kaluza-Klein Monopole
• Exceptional field theory: $SO(5,5)$
• β-supergravity: a ten-dimensional theory with non-geometric fluxes, and its geometric framework
• Flux Compactifications of M-Theory on Twisted Tori
• Supergravities without an Action: Gauging the Trombone
• Massive Type II in Double Field Theory
• Duality Invariance: From M-theory to Double Field Theory
• Tensor Hierarchy and Generalized Cartan Calculus in SL(3)$\times$SL(2) Exceptional Field Theory
• The exceptional story of massive IIA supergravity
• Gauge Symmetry, T-Duality and Doubled Geometry
• Exceptional generalised geometry for massive IIA and consistent reductions
• Seven-branes and Supersymmetry
• An Action for F-theory: $\mathrm{SL}(2)\times {\mathbb{R}}^{+}$ Exceptional Field Theory
• The KK-Monopole/NS5-Brane in Doubled Geometry
• Spectrum-generating Symmetries for BPS Solitons
• Non-geometric branes are DFT monopoles
• Weaving the Exotic Web
• Q7-branes and their coupling to IIB supergravity
• Exotic branes in Exceptional Field Theory: the SL(5) duality group
• Exotic Branes in Exceptional Field Theory: $E_{7(7)}$ and Beyond
• Critical points of maximal D=8 gauged supergravities
• Basics of F-theory from the Type IIB Perspective

Cited by in corpus (1)

• The Geometry, Branes and Applications of Exceptional Field Theory