Non-standard axion electrodynamics and the dual Witten effect

TL;DR

This paper explores non-standard axion electrodynamics derived from SL(2,Z) duality, revealing that such theories imply the existence of dyons, large axion masses, and significant modifications to Higgs physics, thus questioning their phenomenological viability.

Contribution

It demonstrates that non-standard axion couplings can be derived from SL(2,Z) duality but lead to dyons and other phenomenological issues, challenging their viability.

Findings

Non-standard couplings derive from SL(2,Z) duality.

All charged particles become dyons in this framework.

Large axion mass and altered Higgs physics result from these couplings.

Abstract

Standard axion electrodynamics has two closely related features. First, the coupling of a massless axion field to photons is quantized, in units proportional to the electric gauge coupling squared. Second, the equations of motion tell us that a time-dependent axion field in a background magnetic field sources an effective electric current, but a time-dependent axion field in a background electric field has no effect. These properties, which manifestly violate electric-magnetic duality, play a crucial role in experimental searches for axions. Recently, electric-magnetic duality has been used to motivate the possible existence of non-standard axion couplings, which can both violate the usual quantization rule and exchange the roles of electric and magnetic fields in axion electrodynamics. We show that these non-standard couplings can be derived from SL(2,Z) duality, but that they come at a substantial cost: in non-standard axion electrodynamics, all electrically charged particles become dyons when the axion traverses its field range, in a dual form of the standard Witten effect monodromy. This implies that there are dyons near the weak scale, leads to a large axion mass induced by Standard Model fermion loops, and dramatically alters Higgs physics. We conclude that non-standard axion electrodynamics, although interesting to consider in abstract quantum field theory, is not phenomenologically viable.