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.

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Cited by in corpus (1)

• The Geometry, Branes and Applications of Exceptional Field Theory