The Seiberg-Witten Axion

TL;DR

This paper constructs a UV complete model of a Peccei-Quinn axion within Seiberg-Witten theory, revealing how axion couplings are affected by monopoles, duality, and non-perturbative effects, ensuring duality invariance.

Contribution

It introduces a calculable Seiberg-Witten-based model of a PQ axion with magnetic monopoles, demonstrating duality invariance of axion-photon couplings and non-perturbative corrections.

Findings

Axion-photon coupling includes anomaly and periodic monopole-induced terms.

Couplings remain duality invariant across different frames.

Non-perturbative monopole effects modify axion interactions without breaking shift symmetry.

Abstract

We present a fully calculable UV complete toy model of a Peccei-Quinn (PQ) axion coupled to magnetic monopoles as well as electric charges. The theory has manifest electric-magnetic duality built in. We find that the axion-photon coupling contains the usual anomaly term, plus periodic corrections which can also become large if the monopole is light, without violating the discrete axion shift symmetry. These additional periodic terms can be identified as the non-perturbative corrections due to the monopoles (and other BPS states), but can also be interpreted as a sum over instanton corrections. The key aspect helping reconcile axion coupling quantization with electric-magnetic duality is the fact that the axion itself undergoes a non-linear transformation under electric-magnetic duality. The theory analyzed here is just the original $N=2$ supersymmetric $SU(2)$ Seiberg-Witten theory, which contains a PQ axion due to an anomalous spontaneously broken global $R$-symmetry, as well as massless fermionic monopoles and dyons at special points in the moduli space. Hence the entire machinery of the Seiberg-Witten solution can be applied to reliably calculate the photon-axion coupling in different duality frames. We show explicitly that the physically observable axion-photon amplitude is duality invariant, as it had to be.