On Multifield Born and Born-Infeld Theories and their non-Abelian Generalizations

TL;DR

This paper develops a linear auxiliary field formulation for multi-field Born and Born-Infeld theories, enabling the construction of new models and their non-Abelian extensions with manifest symmetries and dualities.

Contribution

It introduces a quadratic Lagrangian framework for multi-field Born-Infeld theories, facilitating the derivation of new models and non-Abelian generalizations with explicit symmetry properties.

Findings

Reproduced known multi-field Born-Infeld theories

Derived new non-linear multi-field models like the n-field Born theory

Constructed non-Abelian extensions with gauge symmetry

Abstract

Starting from a recently proposed linear formulation in terms of auxiliary fields, we study $n$-field generalizations of Born and Born-Infeld theories. In this description the Lagrangian is quadratic in the vector field strengths and the symmetry properties (including the characteristic self-duality) of the corresponding non-linear theory are manifest as on-shell duality symmetries and depend on the choice of the (homogeneous) manifold spanned by the auxiliary scalar fields and the symplectic frame. By suitably choosing these defining properties of the quadratic Lagrangian, we are able to reproduce some known multi-field Born-Infeld theories and to derive new non-linear models, such as the $n$-field Born theory. We also discuss non-Abelian generalizations of these theories obtained by choosing the vector fields in the adjoint representation of an off-shell compact global symmetry group $K$ and replacing them by non-Abelian, $K$-covariant field strengths, thus promoting $K$ to a gauge group.