Single-Flavor Color Superconductivity in a Magnetic Field

a b s t r a c tA range of quantum field theoretical phenomena driven by external magnetic fields and their applications in relativistic systems and quasirelativistic condensed matter ones, such as graphene and Dirac/Weyl semimetals, are reviewed. We start by introducing the underlying physics of the magnetic catalysis. The dimensional reduction of the low-energy dynamics of relativistic fermions in an external magnetic field is explained and its role in catalyzing spontaneous symmetry breaking is emphasized. The general theoretical consideration is supplemented by the analysis of the magnetic catalysis in quantum electrodynamics, chromodynamics and quasirelativistic models relevant for condensed matter physics. By generalizing the ideas of the magnetic catalysis to the case of nonzero density and temperature, we argue that other interesting phenomena take place. The chiral magnetic and chiral separation effects are perhaps the most interesting among them. In addition to the general discussion of the physics underlying chiral magnetic and separation effects, we also review their possible phenomenological implications in heavy-ion collisions and compact stars. We also discuss the application of the magnetic catalysis ideas for the description of the quantum Hall effect in monolayer and bilayer graphene, and conclude that the generalized magnetic catalysis, including both the magnetic catalysis condensates and the quantum Hall ferromagnetic ones, lies at the basis of this phenomenon. We also consider how an external magnetic field affects the underlying physics in a class of three-dimensional quasirelativistic condensed matter systems, Dirac semimetals. While at sufficiently low temperatures and zero density of charge carriers, such semimetals are expected to reveal the regime of the magnetic catalysis, the regime of Weyl semimetals with chiral asymmetry is realized at nonzero density. Finally, we discuss the interplay between relativistic quantum field theories (including quantum electrodynamics and quantum chromodynamics) in a magnetic field and noncommutative field theories, which leads to a new type of the latter, nonlocal noncommutative field theories.

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“…(As for the physics properties of spin-one color superconductors in a magnetic field, some of them are discussed in Refs. [661,662]. )…”

Section: Color Superconductivity In a Magnetic Fieldmentioning

confidence: 94%

Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

2015

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“…(14) and (15) and performing the dk 0 integration (using the Dirac delta functions) followed by using Eqs. (16) and (17) we get the real parts as,…”

Section: ρ 0 Self Energy In the Mediummentioning

confidence: 99%

“…Following Eqs. (16) and (17) we get the thermal self energy functions under external magnetic field which we will denote by a double bar to distinguish them from the thermal self energy functions in the absence of magnetic field. Their explicit expressions are given by…”

Section: ρ 0 Self Energy In the Magnetized Mediummentioning

confidence: 99%

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General structure of the neutral ρ meson self-energy and its spectral properties in a hot and dense magnetized medium

et al. 2019

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The one loop self energy of the neutral ρ meson is obtained for the effective ρππ and ρN N interaction at finite temperature and density in the presence of a constant background magnetic field of arbitrary strength. In our approach, the eB-dependent vacuum part of the self energy is extracted by means of dimensional regularization where the ultraviolet divergences corresponding to the pure vacuum self energy manifest as the pole singularities of gamma as well as Hurwitz zeta functions. This improved regularization procedure consistently reproduces the expected results in the vanishing magnetic field limit and can be used quite generally in other self energy calculations dealing with arbitrary magnetic field strength. In presence of the external magnetic field, the general Lorentz structure for the in-medium vector boson self energy is derived which can also be implemented in case of the gauge bosons such as photons and gluons. It has been shown that with vanishing perpendicular momentum of the external particle, essentially two form factors are sufficient to describe the self energy completely. Consequently, two distinct modes are observed in the study of the effective mass, dispersion relations and the spectral function of ρ 0 where one of the modes possesses two fold degeneracy. For large baryonic chemical potential, it is observed that the critical magnetic field required to block the ρ 0 → π + π − decay channel increases significantly with temperature. However, in case of smaller values reaching down to vanishing chemical potential, the critical field follows the opposite trend.

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“…Recently, the study of color superconductivity in the presence of magnetic fields attracted a lot of attention [21][22][23][24][25]. This interest is primarily driven by potential astrophysical applications, where magnetic fields play an important role.…”

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confidence: 99%

Directional dependence of a color superconducting gap in two-flavor QCD in a magnetic field

Shovkovy

2012

Phys. Rev. D

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We study the effect of a magnetic field on the pairing dynamics in two-flavor color superconducting dense quark matter. The study is performed in the weakly coupled regime of QCD at asymptotically high density, using the framework of Schwinger-Dyson equation in the improved rainbow approximation. We show that the superconducting gap function develops a directional dependence in momentum space. Quasiparticles with momenta perpendicular to the direction of the magnetic field have the largest gaps, while quasiparticles with momenta parallel to the field have the smallest gaps. We argue that the directional dependence is a consequence of a long range interaction in QCD. The quantitative measure of the ellipticity of the gap function is determined by a dimensionless ratio, proportional to the square of the magnetic field and inversely proportional to the fourth power of the quark chemical potential. For magnetic fields in stars, B 10 18 G, the corresponding ratio is estimated to be less than about 10 −2 , justifying the use of the weak magnetic field limit in all stellar applications.

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Single-Flavor Color Superconductivity in a Magnetic Field

Cited by 31 publications

References 22 publications

Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

General structure of the neutral ρ meson self-energy and its spectral properties in a hot and dense magnetized medium

Directional dependence of a color superconducting gap in two-flavor QCD in a magnetic field

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