[Paper Review] Exceptional Field Theory for $E_{6(6)}$ supergravity

Edvard T. Musaev|arXiv (Cornell University)|Mar 29, 2015

Black Holes and Theoretical Physics5 citations

TL;DR

This paper presents a supersymmetric, duality-covariant formulation of E6(6) supergravity using exceptional field theory, realizing the U-duality group E6(6) as a manifest gauge symmetry. By employing exceptional geometric structures, the construction naturally incorporates the tensor hierarchy and yields the complete supersymmetric Lagrangian, unifying duality symmetry and gauge structure in a covariant framework.

ABSTRACT

A brief description of the supersymmetric and duality covariant approach to supergravity is presented. The formalism is based on exceptional geometric structures and turns the hidden U-duality group into a manifest gauge symmetry. Tensor hierarchy of gauged supergravity appears naturally here as a consequence of covariance of the construction. Finally, the full supersymmetric Lagrangian is explicitly constructed. This work was presented on the International Conference Quantum Field Theory and Gravity (QFTG'14) in Tomsk.

Motivation & Objective

• To develop a duality-covariant and supersymmetric formulation of E6(6) supergravity that makes the U-duality group manifest.
• To realize the hidden U-duality symmetry of maximal supergravity as a gauge symmetry through exceptional geometric structures.
• To naturally derive the tensor hierarchy of gauged supergravity as a consequence of the construction's covariance.
• To explicitly construct the full supersymmetric Lagrangian within the exceptional field theory framework.

Proposed method

• Utilizes exceptional geometric structures to extend spacetime and fiber the theory over an extended space with E6(6) covariance.
• Implements a generalized diffeomorphism symmetry that realizes the U-duality group E6(6) as a manifest gauge symmetry.
• Constructs the theory using a covariant action principle that ensures consistency with supersymmetry and duality.
• Introduces a tensor hierarchy via the covariant formulation, where p-form potentials and their gauge transformations emerge naturally.
• Employs a duality-covariant field strength and potential formulation to close the supersymmetry algebra consistently.
• Derives the full Lagrangian by solving the Bianchi identities and closure conditions in the exceptional field theory setup.

Experimental results

Research questions

• RQ1 How can the U-duality group E6(6) be made manifest as a gauge symmetry in E6(6) supergravity?
• RQ2 Can the tensor hierarchy of gauged supergravity be derived naturally from a duality-covariant and supersymmetric construction?
• RQ3 What is the explicit form of the supersymmetric Lagrangian in a framework that unifies duality and gauge symmetry?
• RQ4 How does exceptional field theory enable a consistent and covariant formulation of E6(6) supergravity?

Key findings

• The U-duality group E6(6) is realized as a manifest gauge symmetry through the exceptional field theory framework.
• The tensor hierarchy of gauged supergravity emerges naturally from the covariance of the construction, without ad hoc assumptions.
• The full supersymmetric Lagrangian for E6(6) supergravity is explicitly constructed within the duality-covariant formalism.
• The formulation ensures consistency with both supersymmetry and exceptional geometric covariance, providing a unified description of the theory.