New approach to nonlinear electrodynamics: dualities as symmetries of interaction

TL;DR

This paper introduces a new formulation of nonlinear electrodynamics that makes duality symmetries manifest through auxiliary fields, simplifying the analysis and classification of duality-invariant models.

Contribution

The authors develop a duality-symmetric nonlinear electrodynamics framework using auxiliary tensor fields, providing a clearer off-shell characterization of dualities and new explicit examples.

Findings

Duality symmetry acts linearly on auxiliary fields in the new formulation

The nonlinear U(1) duality condition is equivalent to linear invariance of the interaction function E

New explicit duality-symmetric Lagrangians with auxiliary scalar fields are constructed

Abstract

We elaborate on the duality-symmetric nonlinear electrodynamics in a new formulation with auxiliary tensor fields. The Maxwell field strength appears only in bilinear terms of the corresponding generic Lagrangian, while the self-interaction is presented by a function E depending on the auxiliary fields. Two types of dualities inherent in the nonlinear electrodynamics models admit a simple off-shell characterization in terms of this function. In the standard formulation, the continuous U(1) duality symmetry is nonlinearly realized on the Maxwell field strength. In the new setting, the same symmetry acts as linear U(1) transformations of the auxiliary field variables. The nonlinear U(1) duality condition proves to be equivalent to the linear U(1) invariance of the self-interaction E. The discrete self-duality (or self-duality by Legendre transformation) amounts to a weaker reflection symmetry of E. For a class of duality- symmetric Lagrangians we introduce an alternative representation with the auxiliary scalar field and find new explicit examples of such systems.