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Weyl fermions are two-component chiral fermions in (3+1)-dimensions. Whencoupled to a gauge field, the Weyl fermion is known to have an axial anomaly,which means the current conservation of the left-handed and right-handed Weylfermions cannot be preserved separately. Recently, Weyl fermions have beenproposed in condensed matter systems named as "Weyl semi-metals". In this paperwe propose a Weyl semi-metal phase in magnetically doped topologicalinsulators, and study the axial anomaly in this system. We propose that themagnetic fluctuation in this system plays the role of a "chiral gauge field"which minimally couples to the Weyl fermions with opposite charges for twochiralities. We study the anomaly equation of this sytem and discuss itsphysical consequences, including one-dimensional chiral modes in aferromagnetic vortex line, and a novel plasmon-magnon coupling.

Chiral gauge field and axial anomaly in a Weyl semi-metal