Abstract
We construct analytic (3+1)-dimensional inhomogeneous and topologically non-trivial pion systems using chiral perturbation theory. We discuss the effect of isospin asymmetry with vanishing electromagnetic interactions as well as some particular configurations with non-vanishing electromagnetic interactions. The inhomogeneous configurations of the pion fields are characterized by a non-vanishing topological charge that can be identified with baryons surrounded by a cloud of pions. This system supports a topologically protected persistent superflow. When the electromagnetic field is turned on the superflow corresponds to an electromagnetic supercurrent.
Highlights
One of the main goals of the theoretical and experimental investigations in quantum chromodynamics (QCD) is to determine the phases of hadronic matter as a function of temperature, baryonic density, and isospin asymmetry
We have shown that for a particular condensate ansatz, the complete set of field equations both with and without the minimal coupling to the electromagnetic field can be consistently reduced to integrable equations, where the isospin chemical potential can be related to the system size
We find that the energy density εm, the topological density ρm, and the currents J0, Jφ, and T0φ are constant in the φ direction while they depend nontrivially on the two spatial coordinates r and θ
Summary
One of the main goals of the theoretical and experimental investigations in quantum chromodynamics (QCD) is to determine the phases of hadronic matter as a function of temperature, baryonic density, and isospin asymmetry. A detailed analysis of the electromagnetic interactions of (3 þ 1)-dimensional spatially modulated condensates is not easy; in these situations the only available numerical results on crystals of solitons treat the electromagnetic field as a fixed external field neglecting the back reaction of the hadronic matter It would be an extremely useful result to achieve a sound analytic control on gauged solitons with high topological charge and with crystalline order. In the present paper we use zero temperature gauged twoflavor χPT to construct an analytic (3 þ 1)-dimensional pion inhomogeneous condensate characterized by a nonvanishing topological charge. We achieve this result by an appropriate choice of the condensate ansatz and of the gauge field configuration.
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