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

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.

arXiv comment22 pages, LaTeX source, minor corrections and references added

References in corpus (20)

• On non-abelian generalisation of Born-Infeld action in string theory
• Electric-Magnetic Duality Rotations in Non-Linear Electrodynamics
• New Goldstone multiplet for partially broken supersymmetry
• Partial breaking of global D=4 supersymmetry, constrained superfields, and 3-brane actions
• Spontaneous Breaking of N=2 Global Supersymmetry
• The tensor Goldstone multiplet for partially broken supersymmetry
• Born-Infeld action, supersymmetry and string theory
• New approach to nonlinear electrodynamics: dualities as symmetries of interaction
• On the Euler angles for SU(N)
• Nonlinear Self-Duality in Even Dimensions
• N=2 Born-Infeld Attractors
• Duality Invariant Born-Infeld Theory
• On the dualization of Born-Infeld theories
• Exceptional groups, symmetric spaces and applications
• Doubly Self-Dual Actions in Various Dimensions
• Two-Field Born-Infeld with Diverse Dualities
• Dynamics of D-branes I. The non-Abelian Dirac-Born-Infeld action, its first variation, and the equations of motion for D-branes --- with remarks on the non-Abelian Chern-Simons/Wess-Zumino term
• Observations on BI from $\mathcal{N}=2$ Supergravity and the General Ward Identity
• C-map for Born-Infeld theories
• Shock Wave Polarizations and Optical Metrics in the Born and the Born-Infeld Electrodynamics