The role of the Callan–Witten anomaly density as a Chern–Simons term in Skyrme model*

Abstract

AbstractWe consider axially symmetric solutions of theU(1) gauged Skyrme model supplemented with a Callan–Witten (CW) anomaly density term. The main properties of the solutions are studied, several specific features introduced by the presence of the CW term being identified. We find that the solitons possess a nonzero angular momentum proportional to the electric charge, which in addition to the usual Coulomb part, acquires an extra (topological) contribution from the CW term. Specifically, it is shown that the slope of mass/energyMvs.electric chargeQeand angular momentumJcan be both positiveandnegative. Furthermore, it is shown that the gauged Skyrmion persists even when the quartic (Skyrme) kinetic term disappears.