Exceptional Field Theory III: E$_{8(8)}$

TL;DR

This paper constructs an exceptional field theory for E$_{8(8)}$ that unifies supergravity theories and addresses the dual graviton problem through a novel gauge structure and covariant constraints.

Contribution

It develops the first consistent E$_{8(8)}$ exceptional field theory with a unique gauge-invariant bosonic action including a Chern-Simons term, and demonstrates how it reduces to known supergravity theories.

Findings

Provides a complete bosonic E$_{8(8)}$ exceptional field theory

Introduces a novel Chern-Simons term for gauge vectors

Shows reduction to D=11 and type IIB supergravity theories

Abstract

We develop exceptional field theory for E$_{8(8)}$, defined on a (3+248)-dimensional generalized spacetime with extended coordinates in the adjoint representation of E$_{8(8)}$. The fields transform under E$_{8(8)}$ generalized diffeomorphisms and are subject to covariant section constraints. The bosonic fields include an `internal' dreibein and an E$_{8(8)}$-valued `zweihundertachtundvierzigbein' (248-bein). Crucially, the theory also features gauge vectors for the E$_{8(8)}$ E-bracket governing the generalized diffeomorphism algebra and covariantly constrained gauge vectors for a separate but constrained E$_{8(8)}$ gauge symmetry. The complete bosonic theory, with a novel Chern-Simons term for the gauge vectors, is uniquely determined by gauge invariance under internal and external generalized diffeomorphisms. The theory consistently comprises components of the dual graviton encoded in the 248-bein. Upon picking particular solutions of the constraints the theory reduces to D=11 or type IIB supergravity, for which the dual graviton becomes pure gauge. This resolves the dual graviton problem, as we discuss in detail.