Electric-magnetic duality implies (global) conformal invariance

TL;DR

This paper demonstrates that quantum theories of electric-magnetic duality invariant vector fields in 4D flat spacetime retain conformal invariance upon quantization, extending classical symmetry considerations to the quantum level.

Contribution

It extends Dirac's conditions for relativistic quantum theories to include conformal invariance, showing duality-invariant vector theories remain conformally invariant after quantization.

Findings

Electric-magnetic duality invariant theories are conformally invariant at the quantum level.

Classical conformal invariance persists in quantum theories with manifest duality.

The work generalizes the conditions under which quantum field theories preserve conformal symmetry.

Abstract

We have examined quantum theories of electric magnetic duality invariant vector fields enjoying classical conformal invariance in 4-dimensional flat spacetime. We extend Dirac's argument about "the conditions for a quantum field theory to be relativistic" to "those for a quantum theory to be conformal". We realize that electric magnetic duality invariant vector theories together with classical conformal invariance defined in 4-$d$ flat spacetime are still conformally invariant theories when they are quantized in a way that electric magnetic duality is manifest.