On the robustness of the chiral soliton lattice and the propagation of test quarks

Abstract

In this paper, we demonstrate the robustness of the chiral soliton lattice (ChSL) against a specific class of operators: the higher-order corrections in the 't Hooft large-$N_c$ expansion within the generalized Skyrme model coupled to Maxwell theory. By considering a suitable Ansatz adapted to describe topological solitons at finite baryon density in a constant magnetic field, the generalized Skyrme model coupled to Maxwell theory is reduced to the effective Lagrangian of the ChSL phase, which describes a lattice of domain-walls made of hadrons. One of the key points in this construction is the fact that even when the usual topological charge density vanishes, the presence of the Callan-Witten term in the topological charge density allows for a non-vanishing baryon number. In the present approach, rather than assuming a prescribed external magnetic field (as is usually assumed for the ChSL), we solve the fully coupled Skyrme-Maxwell field equations. Finally, we show how our formulation allows us to study the interaction of the ChSL with test quarks. In particular, we derive the exact analytical spectrum of the Dirac equation in the high-density limit, providing a microscopic characterization of the fermionic excitations within the inhomogeneous hadronic background provided by the ChSL. The comparison of the spectrum of the Dirac operator in the ChSL with that of the standard Dirac operator in a constant magnetic field reveals the fundamental role of both the quark-Skyrmion coupling and the hadronic profile in opening a gap and shifting the spectrum.

V3: The analysis of the interaction of the ChSL with test quarks has been extended. Some plots have been modified