Born duality and strings in hadrodynamics and electrodynamics

Abstract

We propose a dimension-selecting duality principle for electrodynamics and for hadrodynamics of relativistic strings. Dual theories are identical in formal structure to Maxwell's electrodynamics. Maximal dual systems must be two dimensional, with as their simplest examples all the strings of dual-resonance models. Minimal dual systems are realized by Born-Infeld electrodynamics in four dimensions. From these two infinite classes of theories, the added constraints of general covariance and shock-free wave propagation single out uniquely two exceptional systems. One is the Nambu string, the other is the original Born Lagrangian admitting Nambu-string solutions in its strong-field limit. Our analysis stresses the physics and naturalness of string structures in gauge theories. It leads to a geometro-dynamical interpretation of the duality principle.