On supersymmetric E11 exceptional field theory

Abstract

We construct an infinite system of non-linear duality equations, including fermions, that are invariant under global E 11 and gauge invariant under generalised diffeomorphisms upon the imposition of a suitable section constraint. We use finitedimensional fermionic representations of the R-symmetry K(E 11 ) to describe the fermionic contributions to the duality equations. These duality equations reduce to the known equations of E 8 exceptional field theory or eleven-dimensional supergravity for appropriate (partial) solutions of the section constraint. Of key importance in the construction is an indecomposable representation of E 11 that entails extra non-dynamical fields beyond those predicted by E 11 alone, generalising the known constrained p-forms of exceptional field theories. The construction hinges on the tensor hierarchy algebra extension of e 11 , both for the bosonic theory and its supersymmetric extension.

E 9 exceptional field theory. Part II. The complete dynamics

“…The Hodge dual terms in the variations of B and χ follow directly from (5.13). They can also be derived from the gauge transformations in [49], in which the Hodge dual terms and the gauge field transformation (5.36) appear naturally.…”

“…The duality equation (5.35) is a twisted self-duality equation that can be obtained from a truncation of the E 11 twisted self-duality equation defined in [49]. Twisted self-duality in D = 2p dimensions can normally be written as an equality between a p-form field strength dressed with the scalar matrix M ∈ G and its Hodge star contracted with a G-invariant bilinear form.…”

Tensor hierarchy algebras and extended geometry. Part II. Gauge structure and dynamics

“…The purpose of the present paper is to demonstrate how indeed the recently invented tensor hierarchy algebras (THA's) [6,7] are to be seen as the algebraic structure responsible for and underlying extended geometry, in its most general setting. Besides unifying double geometry [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and exceptional geometry , one of the advantages of the framework of extended geometry is that it opens a window to situations with infinite-dimensional structure groups [42][43][44]. Eventually, we would like to establish contact with the E 10 [45] and E 11 [46] proposals.…”

Tensor hierarchy algebras and extended geometry. Part I. Construction of the algebra

“…The invention of the THA's was motivated by the need to accommodate the embedding tensor of gauged supergravities in the algebra [4,5]. It has subsequently become clear [6][7][8][9] that they are also needed as an algebraic basis for models of extended geometry [10]. In certain simple cases, where so called ancillary transformations do not appear, only the corresponding Borcherds superalgebra is needed.…”