| תקציר: | 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 ${\cal N}=2$ supersymmetric $SU(2)$
Seiberg-Witten theory, which contains a PQ axion due to an anomalous
spontaneously broken global $\mathcal{R}$-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. |