Abstract
We study finite isospin chiral perturbation theory (χPT) in a uniform external magnetic field and find the condensation energy of magnetic vortex lattices using the method of successive approximations (originally used by Abrikosov) near the upper critical point beyond which the system is in the normal vacuum phase. The difference between standard Ginzburg–Landau (GL) theory (or equivalently the Abelian Higgs model) and χPT arises due to the presence of additional momentum-dependent (derivative) interactions in χPT and the presence of electromagnetically neutral pions that interact with the charged pions via strong interactions but do not couple directly to the external magnetic field. We find that while the vortex lattice structure is hexagonal similar to vortices in GL theory, the condensation energy (relative to the normal vacuum state in a uniform, external magnetic field) is smaller (larger in magnitude) due to the presence of derivative interactions. Furthermore, we establish that neutral pions do not condense in the vortex lattice near the upper critical field.
Highlights
Quantum Chromodynamics (QCD) is the theory of strong interactions with a very rich phase structure that exhibits chiral symmetry breaking in the QCD vacuum and color confinement
While lattice studies of finite isospin QCD are possible due to the absence of the fermion sign problem, the sign problem reemerges when both isospin and magnetic fields are present simultaneously due to flavor symmetry breaking in the presence of an external electromagnetic field [18], which leads to the loss of γ5 hermicity unless the charges of the up and the down quarks are equal and opposite
We have studied finite isospin χPT in an external magnetic field similar to studies of the Abelian Higgs Model. χPT is richer than the Higgs model due to the presence of derivative interactions, which emerge as a consequence of the symmetry breaking patterns of QCD and the fact that pions are Goldstone modes
Summary
Quantum Chromodynamics (QCD) is the theory of strong interactions with a very rich phase structure that exhibits chiral symmetry breaking in the QCD vacuum and color confinement. We will study the effect of an external uniform magnetic field in the context of finite isospin three-color, two-flavor χPT. While lattice studies of finite isospin QCD are possible due to the absence of the fermion sign problem (unlike at finite baryon chemical potentials), the sign problem reemerges when both isospin and magnetic fields are present simultaneously due to flavor symmetry breaking in the presence of an external electromagnetic field [18], which leads to the loss of γ5 hermicity unless the charges of the up and the down quarks are equal and opposite. We generalize and improve upon the results by considering possible vortex lattice solutions and the corresponding condensation energy (density), relative to the normal vacuum in the presence of a uniform, external magnetic field.
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