# 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 ℝ$^{+}$ ×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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Journal articles

https://hal.archives-ouvertes.fr/hal-02008815
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Submitted on : Tuesday, February 5, 2019 - 9:49:53 PM
Last modification on : Tuesday, January 19, 2021 - 10:26:16 PM

### Citation

Lilian Chabrol. Geometry of $\mathbb{R}^{+}\times E_{3(3)}$ exceptional field theory and F-theory. JHEP, 2019, 08, pp.073. ⟨10.1007/JHEP08(2019)073⟩. ⟨hal-02008815⟩

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