Duality through the symplectic embedding formalism

TL;DR

This paper demonstrates that the symplectic embedding formalism can generate dual equivalent actions by enlarging phase space, revealing a family of duals, and restoring gauge invariance in modified electromagnetic theories.

Contribution

It shows that the symplectic embedding method can produce dual actions similar to the gauging iterative Noether dualization method, with added insights from zero mode arbitrariness.

Findings

The symplectic formalism yields dual actions with extra variables.

The method can restore gauge invariance in broken theories.

It reveals a family of dual equivalent actions.

Abstract

In this work we show that we can obtain dual equivalent actions following the symplectic formalism with the introduction of extra variables which enlarge the phase space. We show that the results are equal as the one obtained with the recently developed gauging iterative Noether dualization method (NDM). We believe that, with the arbitrariness property of the zero mode, the symplectic embedding method (SEM) is more profound since it can reveal a whole family of dual equivalent actions. We illustrate the method demonstrating that the gauge-invariance of the electromagnetic Maxwell Lagrangian broken by the introduction of an explicit mass term and a topological term can be restored to obtain the dual equivalent and gauge-invariant version of the theory.