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

TL;DR

This paper develops a 12-dimensional exceptional field theory based on the group SL(2) x R+ that unifies F-theory and M-theory within a single formalism, providing a new framework for understanding these theories.

Contribution

It constructs an SL(2) x R+ exceptional field theory that encompasses both F-theory and M-theory through a novel 12-dimensional approach.

Findings

The theory imposes a section condition with two solutions: one for 11D supergravity, one for F-theory.

It unifies F-theory and M-theory in a single exceptional field theory framework.

The algebra of local symmetries closes under the section condition.

Abstract

We construct the 12-dimensional exceptional field theory associated to the group $\mathrm{SL}(2) \times \mathbb{R}^+$ . 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 F-theory. Thus $\mathrm{SL}(2) \times \mathbb{R}^+$ exceptional field theory contains both F-theory and M-theory in a single 12-dimensional formalism.