Duality In Equations of Motion from Spacetime Dependent Lagrangians

TL;DR

This paper demonstrates how duality in equations of motion can be derived from spacetime-dependent Lagrangians, unifying abelian and nonabelian dualities, and introduces a method for generating new classical solutions in Yang-Mills theory.

Contribution

It introduces a novel approach to duality via spacetime-dependent Lagrangians, applicable to both abelian and nonabelian cases, and suggests a connection to the holographic principle.

Findings

Duality can be obtained from spacetime-dependent Lagrangians.

The approach applies to both abelian and nonabelian dualities.

A new procedure for classical solutions in Yang-Mills theory is proposed.

Abstract

Starting from lagrangian field theory and the variational principle, we show that duality in equations of motion can also be obtained by introducing explicit spacetime dependence of the lagrangian. Poincare invariance is achieved precisely when the duality conditions are satisfied in a particular way. The same analysis and criteria are valid for both abelian and nonabelian dualities. We illustrate how (1)Dirac string solution (2)Dirac quantisation condition (3)t'Hooft-Polyakov monopole solutions and (4)a procedure emerges for obtaining {\it new} classical solutions of Yang-Mills (Y-M) theory. Moreover, these results occur in a way that is strongly reminiscent of the {\it holographic principle}.