Bispinor Auxiliary Fields in Duality-Invariant Electrodynamics Revisited

TL;DR

This paper revisits the auxiliary bispinor field formulation of duality-invariant nonlinear electrodynamics, extending it to higher derivatives and clarifying the role of twisted self-duality constraints.

Contribution

It extends the auxiliary tensorial field approach to duality-symmetric systems with higher derivatives and clarifies the connection to twisted self-duality constraints.

Findings

The auxiliary field formulation encodes duality symmetry via an invariant interaction Lagrangian.

Higher derivative duality-symmetric systems can be described within this auxiliary field framework.

The twisted self-duality constraints correspond to equations of motion for auxiliary fields.

Abstract

Motivated by a recent progress in studying the duality-symmetric models of nonlinear electrodynamics, we revert to the auxiliary tensorial (bispinor) field formulation of the O(2) duality proposed by us in arXiv:hep-th/0110074, arXiv:hep-th/0303192. In this approach, the entire information about the given duality-symmetric system is encoded in the O(2) invariant interaction Lagrangian which is a function of the auxiliary fields V_{\alpha\beta}, \bar V_{\dot \alpha\dot \beta}. We extend this setting to duality-symmetric systems with higher derivatives and show that the recently employed "nonlinear twisted self-duality constraints" amount to the equations of motion for the auxiliary tensorial fields in our approach. Some other related issues are briefly discussed and a few instructive examples are explicitly worked out.