Include dual magnetic vectors in an N=8 superspace formulation

Develop an N = 8 superspace formulation that incorporates the 28 magnetic dual vector fields alongside the electric vectors so that higher-order corrections can be implemented consistently with non-linear E7(7) duality, including a deformed twisted self-duality constraint, and enabling checks of compatibility with full non-linear supersymmetry.

Background

In four-dimensional N = 8 supergravity, the duality group E7(7) acts on a 56-plet of electric and magnetic vector field strengths, with the dynamics encoded by a twisted self-duality constraint. Non-linear E7(7) is only an on-shell symmetry in standard formulations, and higher-order (counterterm) deformations are expected to require a deformed twisted self-duality condition.

Maintaining full non-linear E7(7) off shell within a superspace framework is obstructed by the absence of a superspace formulation that includes magnetic dual vectors. The Henneaux–Teitelboim approach realizes E7(7) off shell at the expense of manifest Lorentz invariance, but a true N = 8 superspace with both electric and magnetic vectors would be necessary to test non-linear supersymmetry and duality for higher-order invariants.