Thermodynamics of magnetized BPS baryonic layers and the effects of the isospin chemical potential

Through the Hamilton-Jacobi equation of classical mechanics, BPS magnetized baryonic layers (possessing both baryonic charge and magnetic flux) have been constructed in the gauged nonlinear sigma model (G-NLSM) minimally coupled to Maxwell theory. This is one of the most relevant effective theories for quantum chromodynamics (QCD) in the strongly interacting low-energy limit, which also accounts for electromagnetic interactions. Since the topological charge that naturally appears on the right-hand side of the BPS bound is a nonlinear function of the baryonic charge, the thermodynamics of these magnetized baryonic layers is highly nontrivial. In this work, using tools from the theory of the Casimir effect, we derive analytical relationships between baryonic charge, topological charge, magnetic flux, and relevant thermodynamic quantities (such as pressure, specific heat, and magnetic susceptibility) for these layers. The critical baryonic chemical potential is identified. Interestingly, the grand canonical partition function can be related to the Riemann zeta function. On the technical side, it is a remarkable result to derive explicit expressions for all these thermodynamic quantities for a strongly interacting magnetized system at finite baryon density. Moreover, thanks to the BPS property of these configurations, we are also able to analytically determine both the equation of state and the speed of sound. The effects of the isospin chemical potential can also be included; specifically, we are able to explicitly construct the BPS bound and the corresponding BPS configurations even when the isospin chemical potential is nonzero. The physical interpretations of our analytical results are discussed.