Phase boundary of nuclear matter in magnetic field

A bstract Nuclear matter with a strong magnetic field is prevalent inside neutron stars and heavy-ion collisions. In a sufficiently large magnetic field, the ground state is either a chiral soliton lattice (CSL), an array of solitons of the neutral pion field, or a domain-wall Skyrmion phase in which Skyrmions emerge inside the chiral solitons. In the region of large chemical potential and a magnetic field lower than its critical value for CSL, a Skyrmion crystal is expected to take up the ground state based on the chiral perturbation theory at the next leading order. We determine the phase boundary between such a Skyrmion crystal and the QCD vacuum. We examine the previous conjecture that a Skyrmion in magnetic field could be in a form of a neutral pion domain wall bounded by a superconducting ring of charged pions with the radius determined by the quantization condition of the penetrating magnetic flux. We also validate that a Skyrmion would shrink to null without the Skyrme term, although Derrick’s scaling law is modified by a background magnetic field, and the stability at the leading order is not ruled out in theory.