On the electromagnetic hadron current derived from the gauged Wess-Zumino-Witten action

In a recent paper, based on the Skyrme model with the Wess-Zumino-Witten term including electromagnetism, Eto et al. pointed out an intriguing possibility that the Gell-Mann-Nishijima relation is corrected under the presence of back-ground electromagnetic fields, thereby being led to the conclusion that even a neutron acquires non-zero net charge in external magnetic fields. We point out that this remarkable conclusion is inseparably connected with an unwelcome feature of the gauged Wess-Zumino-Witten action, i.e. the non-conservation of source current of Maxwell equation.