Duality invariance implies Poincare invariance

TL;DR

This paper demonstrates that duality invariance in theories with two vector fields in three-dimensional space necessarily leads to Poincare invariance, revealing space-time structure from duality principles.

Contribution

It shows that duality invariance alone constrains the dynamics to be consistent with Poincare symmetry, establishing a fundamental link between duality and space-time structure.

Findings

Duality invariance implies Poincare algebra of the Hamiltonian and momentum.

Space-time symmetry emerges from duality principles.

Theories with duality invariance are necessarily Poincare invariant.

Abstract

We consider all possible dynamical theories which evolve two transverse vector fields out of a three-dimensional Euclidean hyperplane, subject to only two assumptions: (i) the evolution is local in space, and (ii) the theory is invariant under "duality rotations" of the vector fields into one another. The commutators of the Hamiltonian and momentum densities are shown to be necessarily those of the Poincare group or its zero signature contraction. Space-time structure thus emerges out of the principle of duality.