Tensor Hierarchy and Generalized Cartan Calculus in SL(3)$\times$SL(2) Exceptional Field Theory

TL;DR

This paper develops an exceptional field theory for the duality group SL(3)×SL(2), introducing a novel tensor calculus and tensor hierarchy to encode supergravity theories within a 14-dimensional generalized spacetime.

Contribution

It constructs a new exceptional field theory with an advanced tensor hierarchy and a Cartan-like calculus, extending previous formulations to higher degrees.

Findings

Systematic development of a higher-degree tensor hierarchy.

Introduction of a covariant nil-potent differential calculus.

Encoding of full D=11 and type IIB supergravity.

Abstract

We construct exceptional field theory for the duality group SL(3)$\times$SL(2). The theory is defined on a space with 8 `external' coordinates and 6 `internal' coordinates in the $(3,2)$ fundamental representation, leading to a 14-dimensional generalized spacetime. The bosonic theory is uniquely determined by gauge invariance under generalized external and internal diffeomorphisms. The latter invariance can be made manifest by introducing higher form gauge fields and a so-called tensor hierarchy, which we systematically develop to much higher degree than in previous studies. To this end we introduce a novel Cartan-like tensor calculus based on a covariant nil-potent differential, generalizing the exterior derivative of conventional differential geometry. The theory encodes the full $D=11$ or type IIB supergravity, respectively.