Papers by Vladimir Miransky
Physics Reports, 2015
A range of quantum field theoretical phenomena driven by external magnetic fields and their appli... more A 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.
Mod Phys Lett a, 2004
The linear $SU(2)_L \times SU(2)_R$ sigma-model occupies a unique place in elementary particle ph... more The linear $SU(2)_L \times SU(2)_R$ sigma-model occupies a unique place in elementary particle physics and quantum field theory. It has been recently realized that when a chemical potential for hypercharge is added, it becomes a toy model for the description of the dynamics of the kaon condensate in high density QCD. We review recent results in nonperturbative dynamics obtained in the ungauged and gauged versions of this model.
Phys Rev D, 1995
It is shown that chiral symmetry is spontaneously broken by a constant magnetic field in QED. The... more It is shown that chiral symmetry is spontaneously broken by a constant magnetic field in QED. The dynamical mass of fermions (energy gap in the fermion spectrum) is mdyn~=C √eB exp[-(π/α)1/2], where B is the magnetic field, the constant C is of order one, and α=e2/4π is the renormalized coupling constant. Possible applications of this effect are discussed.
Physical Review D Particles and Fields, Jan 28, 2009
We introduce a new class of models describing the quark mass hierarchy. In this class, the dynami... more We introduce a new class of models describing the quark mass hierarchy. In this class, the dynamics primarily responsible for electroweak symmetry breaking (EWSB) leads to the mass spectrum of quarks with no (or weak) isospin violation. Moreover, the values of these masses are of the order of the observed masses of the down-type quarks. Then, strong (although subcritical) horizontal diagonal interactions for the t quark plus horizontal flavor-changing neutral interactions between different families lead (with no fine-tuning) to a realistic quark mass spectrum. In this scenario, many composite Higgs bosons occur. A concrete model with the dynamical EWSB with the fourth family is described in detail.
Phys Rev B, 2010
Utilizing the Baym-Kadanoff formalism with the polarization function calculated in the random pha... more Utilizing the Baym-Kadanoff formalism with the polarization function calculated in the random phase approximation, the dynamics of the $\nu=0$ quantum Hall state in bilayer graphene is analyzed. Two phases with nonzero energy gap, the ferromagnetic and layer asymmetric ones, are found. The phase diagram in the plane $(\tilde{\Delta}_0,B)$, where $\tilde{\Delta}_0$ is a top-bottom gates voltage imbalance, is described. It is shown that the energy gaps in these phases scale linearly, $\Delta E\sim 10 B[T]K, with magnetic field. The comparison of these results with recent experiments in bilayer graphene is presented.
On Gauge Theories with Additional Four-Fermion Interaction
Mod Phys Lett a, 1989
In the ladder QED with four-fermion interaction, the anomalous dimension γm of the operator bar ψ... more In the ladder QED with four-fermion interaction, the anomalous dimension γm of the operator bar ψ ψ is calculated on the full critical line. It is shown that in the nonperturbative phase with the gauge coupling α(0)< αc = π/3, the dynamical dimension d{bar ψ ψ } =3 -γ m is smaller than two (γm > 1) near the critical line. This suggests that gauge theories with fourfermion interaction may be renormalizable. The applications of these theories to the technicolor models are discussed.
Phys Rev Lett, 1996
It is shown that in 2+ 1 dimensions, a constant magnetic field is a strong catalyst of dynamical ... more It is shown that in 2+ 1 dimensions, a constant magnetic field is a strong catalyst of dynamical flavor symmetry breaking, leading to generating a fermion dynamical mass even at the weakest attractive interaction between fermions. The effect is illustrated in the Nambu-Jona-Lasinio model in a magnetic field. The low-energy effective action in this model is derived and the thermodynamic properties of the model are established.
Physics Letters B, 1987
In non-asymptotically free gauge theories with a non-trivial ultraviolet fixed point, scale symme... more In non-asymptotically free gauge theories with a non-trivial ultraviolet fixed point, scale symmetry breaking (the scale anomaly) caused by the non-perturbative PCAC dynamics is studied. In the two-loop approximation the analytical expression for the gluon condensate is obtained. It is shown that the form of the anomaly depends on the type of phase of the theory to which it relates. The hypothesis about the soft behaviour at small distances of composite operators in such theories is confirmed.
Physical review D: Particles and fields, Jan 15, 1995
It is shown that in 2 + 1 dimensions, a constant magnetic field is a strong catalyst of dynamical... more It is shown that in 2 + 1 dimensions, a constant magnetic field is a strong catalyst of dynamical flavor symmetry breaking, leading to generating a fermion dynamical mass even at the weakest attractive interaction between fermions. The essence of this effect is that in a magnetic field, in 2 + 1 dimensions, the dynamics of fermion pairing is essentially onedimensional. The effect is illustrated in the Nambu-Jona-Lasinio model in a magnetic field.
Graphene and graphene-based nanostructures
Physical Review B, 2002
A theory of the magnetic field driven (semi-)metalinsulator phase transition is developed for pla... more A theory of the magnetic field driven (semi-)metalinsulator phase transition is developed for planar systems with a low density of carriers and a linear (i.e., relativistic like) dispersion relation for low energy quasiparticles. The general structure of the phase diagram of the theory with respect to the coupling constant, the chemical potential and temperature is derived in two cases, with and without an external magnetic field. The conductivity and resistivity as functions of temperature and magnetic field are studied in detail. An exact relation for the value of the "offset" magnetic field Bc, determining the threshold for the realization of the phase transition at zero temperature, is established. The theory is applied to the description of a recently observed phase transition induced by a magnetic field in highly oriented pyrolytic graphite. 71.30.+h,
Response of Dense Relativistic Matter to a Magnetic Field
Progress of Theoretical Physics Supplement, 2010
The properties of the ground state of dense relativistic matter in a magnetic field are examined ... more The properties of the ground state of dense relativistic matter in a magnetic field are examined as a function of the temperature and the chemical potential. The dynamical generation of the chiral shift parameter in the normal ground state is studied. Possible implications of the revealed structure of the normal ground state on the physics of protoneutron stars are briefly mentioned.
Progress of Theoretical Physics, 2000
In view of the successful asymptotic Padé-approximant predictions for higher-loop terms within QC... more In view of the successful asymptotic Padé-approximant predictions for higher-loop terms within QCD and massive scalar field theory, we address whether Padé-summations of the M S QCD β-function for a given number of flavours exhibit an infrared-stable fixed point, or alternatively, an infrared attractor of a double valued couplant as noted by Kogan and Shifman for the case of supersymmetric gluodynamics. Below an approximant-dependent flavour threshold (6 ≤ n f ≤ 8), we find that Padé-summation β-functions incorporating [2|1], [1|2], [2|2], [1|3], and [3|1] approximants whose Maclaurin expansions match known higher-than-one-loop contributions to the β-function series always exhibit a positive pole prior to the occurrence of their first positive zero, precluding any identification of this first positive zero as an infrared-stable fixed point of the β-function. This result is shown to be true regardless of the magnitude of the presently-unknown five-loop β-function contribution explicitly appearing within Padé-summation β-functions incorporating [2|2], [1|3], and [3|1] approximants. Moreover, the pole in question suggests the occurrence of dynamics in which both a strong and an asymptotically-free phase share a common infrared attractor. We briefly discuss the possible relevance of infrared-attractor dynamics to the success of recent calculations of the glueball mass spectra in QCD with Nc → ∞ via supergravity. As n f increases above an approximant-dependent flavour threshold, Padé-summation β-functions incorporating [2|2], [1|3], and [3|1] approximants exhibit dynamics controlled by an infrared-stable fixed point over a widening domain of the five-loop M S β-function parameter (β4/β0). Subsequent to the above-mentioned flavour threshold, all approximants considered exhibit infrared-stable fixed points that decrease in magnitude with increasing flavour number. k j=1 R j x j specifies all coefficients within [N |M ]approximants to the series only for {N, M } such that k = N + M ; even four-loop calculations (corresponding to k = 3 if the leading x 2 behaviour is factored out from the series) serve only to specify [2|1], [1|2], and [0|3]
Physics Letters B, 2004
The linear σ-model with a chemical potential for hypercharge is a toy model for the description o... more The linear σ-model with a chemical potential for hypercharge is a toy model for the description of the dynamics of the kaon condensate in high density QCD. We analyze the dynamics of the gauged version of this model. It is shown that spontaneous breakdown of SU (2) × U (1)Y symmetry, caused by the chemical potential, is always accompanied by spontaneous breakdown of both rotational symmetry and electromagnetic U (1)em. The spectrum of excitations in this model is rich and, because of rotational symmetry breakdown, anisotropic. It is shown that there exist excitation branches that behave as phonon like quasiparticles for small momenta and as roton like ones for large momenta. This suggests that this model can be relevant for anisotropic superfluid systems.
Physics Letters B, 1995
It is shown that in 3 + 1 dimensions, a constant magnetic field is a catalyst of dynamical chiral... more It is shown that in 3 + 1 dimensions, a constant magnetic field is a catalyst of dynamical chiral symmetry breaking, leading to generating a fermion mass even at the weakest attractive interaction between fermions. The essence of this effect is the dimensional reduction D → D − 2 (3 + 1 → 1 + 1) in the dynamics of fermion pairing in a magnetic field. The effect is illustrated in the Nambu-Jona-Lasinio model. Possible applications of this effect are briefly discussed.
Physical Review Letters, 2002
We describe a class of relativistic models incorporating a finite density of matter in which spon... more We describe a class of relativistic models incorporating a finite density of matter in which spontaneous breakdown of continuous symmetries leads to a lesser number of Nambu-Goldstone bosons than that required by the Goldstone theorem. This class, in particular, describes the dynamics of the kaon condensate in the color-flavor locked phase of high density QCD. We describe the spectrum of low energy excitations in this dynamics and show that, despite the presence of a condensate and gapless excitations, this system is not a superfluid.
Physical Review Letters, 1999
We describe a (first, to the best of our knowledge) essentially soluble example of dynamical symm... more We describe a (first, to the best of our knowledge) essentially soluble example of dynamical symmetry breaking phenomenon in a 3+1 dimensional gauge theory without fundamental scalar fields: QED in a constant magnetic field. 11.30. Rd, 11.30.Qc, Recently the magnetic catalysis of dynamical chiral symmetry breaking has been established as a universal phenomenon in 2+1 and 3+1 dimensions: a constant magnetic field leads to the generation of a fermion dynamical mass even at the weakest attractive interaction between fermions [1-3]. The essence of this effect is the dimensional reduction D → D − 2 in the dynamics of fermion pairing in a magnetic field: at weak coupling, this dynamics is dominated by the lowest Landau level (LLL) which is essentially (D − 2)-dimensional [1-3]. The effect may have interesting applications in condensed matter physics [4] and cosmology .
Physical Review Letters, 1994
It is shown that in 2+ 1 dimensions, a constant magnetic field is a strong catalyst of dynamical ... more It is shown that in 2+ 1 dimensions, a constant magnetic field is a strong catalyst of dynamical flavor symmetry breaking, leading to generating a fermion dynamical mass even at the weakest attractive interaction between fermions. The effect is illustrated in the Nambu-Jona-Lasinio model in a magnetic field. The low-energy effective action in this model is derived and the thermodynamic properties of the model are established.
Physical Review D, 2012
The ATLAS and CMS experiments have recently discovered a new 125 GeV boson. We show that the prop... more The ATLAS and CMS experiments have recently discovered a new 125 GeV boson. We show that the properties of this particle, including the enhancement of its diphoton decay rate, can be explained in a model with an isospin symmetric Higgs boson. The predictions of the model relevant for future experiments are also discussed.
Physical Review D, 2000
The problem of color superconductivity in dense QCD is reconsidered in the improved rainbow appro... more The problem of color superconductivity in dense QCD is reconsidered in the improved rainbow approximation to the Schwinger-Dyson equation. The effect of the unscreened magnetic modes of gluons on the value of the color condensate is studied. In particular, it is shown that, at sufficiently large values of the chemical potential, these modes lead to the enhancement of the superconducting order parameter. The interplay between the instanton induced interaction and the one-gluon induced one in color superconductivity is discussed. 11.15.Ex, 12.38.Aw, 26.60.+c
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Papers by Vladimir Miransky