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

## TL;DR

This paper develops an $SL(2)\times\mathbb{R}^+$ exceptional field theory in 12 dimensions that unifies F-theory and M-theory through a common covariant framework, revealing new insights into dualities.

## Contribution

It presents the first explicit action for an $SL(2)\times\mathbb{R}^+$ exceptional field theory, unifying F-theory and M-theory in a single formalism.

## Key findings

- The theory enforces a section condition with two solutions, corresponding to 11D supergravity and Type IIB supergravity.
- The formalism makes U-duality symmetries manifest in a 12-dimensional setting.
- Provides a covariant action that encapsulates both F-theory and M-theory.

## Abstract

Exceptional Field Theory employs an extended spacetime to make supergravity fully covariant under the U-duality groups of M-theory. The 12-dimensional EFT associated to the group $SL(2)\times\mathbb{R}^+$ together with its action is presented. 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 Type IIB supergravity and F-theory. Thus $SL(2)\times\mathbb{R}^+$ Exceptional Field Theory contains both F-theory and M-theory in a single 12-dimensional formalism.