Bispinor Auxiliary Fields in Duality-Invariant Electrodynamics Revisited: The U(N) Case

Understand

We update and detail the formulation of the duality-invariant systems of N interacting abelian gauge fields with N auxiliary bispinor fields added.

• In this setting, the self-duality amounts to U(N) invariance of the nonlinear interaction of the auxiliary fields.
• The U(N) self-dual Lagrangians arise after solving the nonlinear equations of motion for the auxiliary fields.
• We also elaborate on a new extended version of the bispinor field formulation involving some additional scalar auxiliary fields and study U(N) invariant interactions with derivatives of the auxiliary bispinor fields.