Solitons in the gauged Skyrme-Maxwell model

Abstract

We consider soliton solutions of the U (1) gauged Skyrme model with the pion mass term. The domain of existence of gauged Skyrmions is restricted from above by the value of the pion mass. Concentrating on the solutions of topological degree one, we find that coupling to the electromagnetic field breaks the symmetry of the configurations, the Skyrmions carrying both an electric charge and a magnetic flux, with an induced dipole magnetic moment. The Skyrmions also possess an angular momentum, which is quantized in the units of the electric charge. The mass of the gauged Skyrmions monotonically decreases with increase of the gauge coupling.

Geometry of gauged skyrmions

“…[1,2,16,17]). Of particular interest in physicallyrealistic models is the inclusion of a potential term which gives the pion mass [3], and recently some work has been done in understanding gauged skyrmions with massive pions [18]. It would be interesting to consider all of these generalised Skyrme models within a geometric framework in a similar vein to what we have described here.…”

“…The Skyrme field φ : R 3 → S 3 can be coupled to a gauge field [4,8,9,10,11,12,13,14,18,21,22] . Much of the work on the gauged Skyrme model seeks to model interactions between nucleons and electromagnetic fields, in which case the gauge group U(1) is most natural, but other choices of gauge group have also been studied.…”

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

“…and boundary values f(0) = π , f(∞) = 0, the integral of ϱ 0 equals the integer (winding number) n. Most importantly, this number q = n presents a lower bound 9 on the energy of the Skyrmion on R 3 .…”

“…More recently, SO(2) gauged Skyrmions 5 in 3 + 1 dimensions were studied quantitatively in [7,8] (see also [9]). These solitons carry both electric charge Q e [7] and angular momentum J [8], and are characterised by the asymptotic value of the electric component A 0 of the Maxwell potential A µ .…”

On the effects of the Chern-Simons term in an Abelian gauged Skyrme model in d = 4 + 1 dimensions

“…More recently, SO(2) gauged Skyrmions 1 in 3 + 1 dimensions were studied quantitatively in Refs. [7,8] (see also [9]). These solitons carry both electric charge Q e [7] and angular momentum J [8], and are characterised by the asymptotic value of the electric component A 0 of the Maxwell potential A µ .…”