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

TL;DR

This paper revisits the formulation of duality-invariant electrodynamics with multiple gauge fields, introducing auxiliary bispinor and scalar fields to generate U(N) invariant self-dual theories, including higher-derivative extensions.

Contribution

It extends the bispinor auxiliary field approach to N interacting gauge fields, incorporating scalar auxiliaries and derivative interactions to produce new U(N) self-dual models.

Findings

Derived U(N) invariant self-dual Lagrangians from auxiliary field equations.

Developed an extended bispinor formulation with scalar auxiliary fields.

Constructed higher-derivative U(N) self-dual theories.

Abstract

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. Such interactions generate higher-derivative U(N) self-dual theories.