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.
Highlights
While DFT encodes the fully doubled spacetime coordinates in an O(10, 10) vector, the formulation of EFT is based on a split of the coordinates into ‘external’ and ‘internal’ directions and a corresponding decomposition of the tensor fields, as in Kaluza-Klein compactifications
EFTs with duality groups Ed(d) have been constructed explicitly for d = 6, 7, 8, in which case the tensor hierarchy needed for constructing an action is rather short: it ends with the 2-forms for d = 6, 7 and with 1-forms for d = 8.1 In this paper, we investigate the case of a smaller duality groups Ed(d)
The use of fields depending on extended coordinates subject to a section constraint in this way is well motivated by string theory: in string field theory on toroidal backgrounds, the string field depends both on momentum and winding coordinates, transforming covariantly under the T-duality group, subject to the level-matching constraint
Summary
We define the generalized Lie derivatives governing generalized (internal) diffeomorphisms and their ‘E-bracket’ gauge algebra.
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