Abstract
The Chiral Soliton Lattice (CSL) is a state with a periodic array of topological solitons that spontaneously breaks parity and translational symmetries. Such a state is known to appear in chiral magnets. We show that CSL also appears as a ground state of quantum chromodynamics at nonzero chemical potential in a magnetic field. By analyzing the fluctuations of the CSL, we furthermore demonstrate that in strong but achievable magnetic fields, charged pions undergo Bose-Einstein condensation. Our results, based on a systematic low-energy effective theory, are model-independent and fully analytic.
Highlights
Pion dynamics in strong magnetic fields generates the Chiral Soliton Lattice (CSL) with broken continuous translational symmetry, leading to a phonon as the Nambu-Goldstone boson
We show that CSL appears as a ground state of quantum chromodynamics at nonzero chemical potential in a magnetic field
Pion dynamics in strong magnetic fields generates the CSL with broken continuous translational symmetry, leading to a phonon as the Nambu-Goldstone boson
Summary
The low-energy dynamics of QCD is dominated by the spontaneously broken chiral symmetry, and can be described by an effective theory for the ensuing Nambu-Goldstone bosons (pions): the chiral perturbation theory. The predictions of this effective theory are organized by a derivative expansion, controlled by the parameter p/(4πfπ), where p is a characteristic momentum and fπ is the pion decay constant [6, 7]. Σ is a 2 × 2 unitary matrix containing the pion degrees of freedom It couples to an external electromagnetic gauge field Aμ via the covariant derivative DμΣ ≡ ∂μΣ − i[Qμ, Σ], where. Note that the scale pCSL can be arbitrarily small, creating a hierarchy of scales for symmetry breaking
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