E7(7) exceptional field theory in superspace

Abstract

We formulate the locally supersymmetric E 7(7) exceptional field theory in a (4 + 56|32) dimensional superspace, corresponding to a 4D N = 8 "external" superspace augmented with an "internal" 56-dimensional space. This entails the unification of external diffeomorphisms and local supersymmetry transformations into superdiffeomorphisms. The solutions to the superspace Bianchi identities lead to on-shell duality equations for the p-form field strengths for p ≤ 4. The reduction to component fields provides a complete description of the on-shell supersymmetric theory. As an application of our results, we perform a generalized Scherk-Schwarz reduction and obtain the superspace formulation of maximal gauged supergravity in four dimensions parametrized by an embedding tensor.

On supersymmetric E11 exceptional field theory

“…give the supercovariantisation of the scalar field momentum P ijkl a [7,82], while the last two terms represent the supercovariantisation of the 3-form field strength H ijkl abc [81]. Similarly, O abc i j is the supercovariantisation of the 3-form field strength H abc i j [81]. This is consistent with the duality equation relating the scalar field current and the 3-form field strength in the adjoint representation.…”

“…We also check in Appendix E that the fermion bilinear decomposed under Spin(1, 3) × SU (8) gives consistently the supercovariantisation of the field strengths in E 7 exceptional field theory [80,81].…”

“…The absence of undesirable representations determines the relative coefficients in O ij ab , which in turn reproduces the supercovariantisation of the twisted self-duality equation in N = 8 supergravity [82]. give the supercovariantisation of the scalar field momentum P ijkl a [7,82], while the last two terms represent the supercovariantisation of the 3-form field strength H ijkl abc [81]. Similarly, O abc i j is the supercovariantisation of the 3-form field strength H abc i j [81].…”

“…E K(E 11 ) fermions under Spin(1, 3) × SU (8) In this appendix, we perform the decomposition of the K(E 11 ) spinors under Spin(1, 3) × SU (8) associated with exceptional field theory in four external dimensions. We use this to probe the action of generalised diffeomorphisms discussed in (7.18) and compare with results available in the literature for the supersymmetric E 7 exceptional field theory [80,81].…”

A master exceptional field theory

“…Although these higher forms do not need to be introduced in exceptional field theory in order to write a (pseudo)-Lagrangian for the dynamical fields, they are naturally defined as dual potentials. The three-form and four-form field strengths were for example introduced in E 7 exceptional field theory in [126], and it is clear from representation theory that the corresponding duality equations would be part of the E 11 exceptional field theory duality equation in the GL( 4) × E 7 decomposition.…”