Geometry of ℝ+ × E3(3) exceptional field theory and F-theory

Abstract

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.