The Geometry, Branes and Applications of Exceptional Field Theory

TL;DR

Exceptional field theory extends traditional geometry to unify supergravity fields and symmetries, simplifying duality solutions and enabling exploration of exotic M-theory phenomena like non-geometric spaces and exotic branes.

Contribution

This review introduces exceptional field theory as a unifying geometric framework for supergravity, revealing hidden symmetries and simplifying duality solution classifications.

Findings

Unified supergravity fields via extended geometry

Simplified duality orbits into geometric objects

Exploration of exotic branes and non-geometric spaces

Abstract

This is a review of exceptional field theory: a generalisation of Kaluza-Klein theory that unifies the metric and $p$-form gauge field degrees of freedom of supergravity into a generalised or extended geometry, whose additional coordinates may be viewed as conjugate to brane winding modes. This unifies the maximal supergravities, treating their previously-hidden exceptional Lie symmetries as a fundamental geometric symmetry. Duality orbits of solutions simplify into single objects, that in many cases have simple geometric interpretations, for instance as wave or monopole-type solutions. It also provides a route to explore exotic or non-geometric aspects of M-theory, such as exotic branes, U-folds, and more novel sorts of non-Riemannian spaces.