arXiv subjects

E. V. Gorbar

Publications and source records attributed to E. V. Gorbar.

At least 127 records · Page 7Linked to original sources

arXiv2007

Gap generation for Dirac fermions on Lobachevsky plane in a magnetic field

We study symmetry breaking and gap generation for fermions in the 2D space of constant negative curvature (the Lobachevsky plane) in an external covariantly constant magnetic field in a four-fermion model. It is shown that due to the magnetic and negative curvature catalysis phenomena the critical coupling constant is zero and there is a symmetry breaking condensate in the chiral limit even in free theory. We analyze solutions of the gap equation in the cases of zero, weak, and strong magnetic fields. As a byproduct we calculate the density of states and the Hall conductivity for noninteracting fermions that may be relevant for studies of graphene.

hep-ph↗

arXiv2007

Gluonic phases, vector condensates, and exotic hadrons in dense QCD

We study the dynamics in phases with vector condensates of gluons (gluonic phases) in dense two-flavor quark matter. These phases yield an example of dynamics in which the Higgs mechanism is provided by condensates of gauge (or gauge plus scalar) fields. Because vacuum expectation values of spatial components of vector fields break the rotational symmetry, it is naturally to have a spontaneous breakdown both of external and internal symmetries in this case. In particular, by using the Ginzburg-Landau approach, we establish the existence of a gluonic phase with both the rotational symmetry and the electromagnetic U(1) being spontaneously broken. In other words, this phase describes an anisotropic medium in which the color and electric superconductivities coexist. It is shown that this phase corresponds to a minimum of the Ginzburg-Landau potential and, unlike the two-flavor superconducting (2SC) phase, it does not suffer from the chromomagnetic instability. The dual (confinement) description of its dynamics is developed and it is shown that there are light exotic vector hadrons in the spectrum, some of which condense. Because most of the initial symmetries in this system are spontaneously broken, its dynamics is very rich.

hep-ph↗

arXiv2006

Collective excitations, instabilities, and ground state in dense quark matter

We study the spectrum of light plasmons in the (gapped and gapless) two-flavor color superconducting phases and its connection with the chromomagnetic instabilities and the structure of the ground state. It is revealed that the chromomagnetic instabilities in the 4-7th and 8th gluonic channels correspond to two very different plasmon spectra. These spectra lead us to the unequivocal conclusion about the existence of gluonic condensates (some of which can be spatially inhomogeneous) in the ground state. We also argue that spatially inhomogeneous gluonic condensates should exist in the three-flavor quark matter with the values of the mass of strange quark corresponding to the gapless color-flavor locked state.

hep-ph↗

arXiv2006

Vortices in gauge models at finite density with vector condensates

There exists a class of gauge models incorporating a finite density of matter in which the Higgs mechanism is provided by condensates of gauge (or gauge and scalar) fields, i.e., there are vector condensates in this case. We describe vortex solutions in the simplest model in this class, the gauged $SU(2)\times U(1)_Y$ $σ$-model with the chemical potential for hypercharge $Y$, in which the gauge symmetry is completely broken. It is shown that there are three types of topologically stable vortices in the model, connected either with photon field or hypercharge gauge field, or with both of them. Explicit vortex solutions are numerically found and their energy per unit length are calculated. The relevance of these solutions for the gluonic phase in the dense two-flavor QCD is discussed.

hep-ph↗

arXiv2005

Neutral Larkin--Ovchinnikov--Fulde--Ferrell state and chromomagnetic instability in two-flavor dense QCD

In two-flavor dense quark matter, we describe the dynamics in the single plane wave Larkin--Ovchinnikov--Fulde--Ferrell (LOFF) state satisfying the color and electric neutrality conditions. We find that because the neutral LOFF state itself suffers from a chromomagnetic instability in the whole region where it coexists with the (gapped/gapless) two-flavor superconducting (2SC/g2SC) phases, it cannot cure this instability in those phases. This is unlike the recently revealed gluonic phase which seems to be able to resolve this problem.

hep-ph↗

arXiv2005

Gluonic phase in neutral two-flavor dense QCD

In the Ginzburg-Landau approach, we describe a new phase in neutral two-flavor quark matter in which gluonic degrees of freedom play a crucial role. We call it a gluonic phase. In this phase gluonic dynamics cure a chromomagnetic instability in the 2SC solution and lead to spontaneous breakdown of the color gauge symmetry, the electromagnetic U(1), and the rotational SO(3). In other words, the gluonic phase describes an anisotropic medium in which the color and electric superconductivities coexist. Because most of the initial symmetries in this system are spontaneously broken, its dynamics is very rich.

hep-ph↗

arXiv2005

Chiral dynamics in QED and QCD in a magnetic background and nonlocal noncommutative field theories

We study the connection of the chiral dynamics in QED and QCD in a strong magnetic field with noncommutative field theories (NCFT). It is shown that these dynamics determine complicated nonlocal NCFT. In particular, although the interaction vertices for electrically neutral composites in these gauge models can be represented in the space with noncommutative spatial coordinates, there is no field transformation that could put the vertices in the conventional form considered in the literature. It is unlike the Nambu-Jona-Lasinio (NJL) model in a magnetic field where such a field transformation can be found, with a cost of introducing an exponentially damping form factor in field propagators. The crucial distinction between these two types of models is in the characters of their interactions, being short-range in the NJL-like models and long-range in gauge theories. The relevance of the NCFT connected with the gauge models for the description of the quantum Hall effect in condensed matter systems with long-range interactions is briefly discussed.

hep-th↗

arXiv2005

Nondecoupling phenomena in QED in a magnetic field and noncommutative QED

The dynamics in QED in a strong constant magnetic field and its connection with the noncommutative QED are studied. It is shown that in the regime with the lowest Landau level (LLL) dominance the U(1) gauge symmetry in the fermion determinant is transformed into the noncommutative $U(1)_{nc}$ gauge symmetry. In this regime, the effective action is intimately connected with that in noncommutative QED and the original U(1) gauge Ward identities are broken (the LLL anomaly). On the other hand, it is shown that although a contribution of each of an infinite number of higher Landau levels is suppressed in an infrared region, their cumulative contribution is not (a nondecoupling phenomenon). This leads to a restoration of the original U(1) gauge symmetry in the infrared dynamics. The physics underlying this phenomenon reflects the important role of a boundary dynamics at spatial infinity in this problem.

hep-th↗

arXiv2004

Dynamical Symmetry Breaking on a Cylinder in Magnetic Field

We study dynamical symmetry breaking on a cylinder in external magnetic field parallel to the axis of cylinder when magnetic field affects the dynamics of fermions only through the Aharonov-Bohm phase. We find that unlike other previously studied cases magnetic field in our case counteracts the generation of dynamical fermion mass which decreases with magnetic field. There exists also a purely kinematical contribution to the fermion gap which grows linearly with magnetic field. Remarkably, we find that the total fermion gap, which includes both the dynamical and kinematical contributions, always increases with magnetic field irrespectively the values of coupling constant and the radius of cylinder. Thus, although the dynamical mass is suppressed, external magnetic field does enhance the total fermion gap in the spectrum.

hep-ph↗

arXiv2004

Relativistic field theories in a magnetic background as noncommutative field theories

We study the connection of the dynamics in relativistic field theories in a strong magnetic field with the dynamics of noncommutative field theories (NCFT). As an example, the Nambu-Jona-Lasinio models in spatial dimensions $d \geq 2$ are considered. We show that this connection is rather sophisticated. In fact, the corresponding NCFT are different from the conventional ones considered in the literature. In particular, the UV/IR mixing is absent in these theories. The reason of that is an inner structure (i.e., dynamical form-factors) of neutral composites which plays an important role in providing consistency of the NCFT. An especially interesting case is that for a magnetic field configuration with the maximal number of independent nonzero tensor components. In that case, we show that the NCFT are finite for even $d$ and their dynamics is quasi-(1+1)-dimensional for odd $d$. For even $d$, the NCFT describe a confinement dynamics of charged particles. The difference between the dynamics in strong magnetic backgrounds in field theories and that in string theories is briefly discussed.

hep-th↗

arXiv2003

Universality and Ambiguities of the Conformal Anomaly

The one-loop structure of the trace anomaly is investigated using different regularizations and renormalization schemes: dimensional, proper time and Pauli-Villars. The universality of this anomaly is analyzed from a very general perspective. The Euler and Weyl terms of the anomalous trace of the stress tensor are absolutely universal. The pure derivative $ \square R$-term is shown to be universal only if the regularization breaks conformal symmetry softly. If the breaking of conformal symmetry by the regularization method is hard the coefficient of this term might become arbitrary which points out the presence of an ambiguous $ \int\sqrt{-g} R^2$-term in the effective quantum action. These ambiguities arise in some prescriptions of dimensional and Pauli-Villars regularizations. We discuss the implications of these results for anomaly-induced inflationary scenarios and AdS/CFT correspondence.

hep-th↗

arXiv2003

Fractal structure of the effective action in (quasi-) planar models with long-range interactions

We derive the effective potential for composite fields in a class of (quasi-) planar models with long-range interactions. This class of models can be relevant for high temperature superconductors and graphite. The fractal structure of the effective potential is revealed and its physical interpretation is presented. It is argued that the multi-branched fractal structure of the potential reflects the presence of an infinite tower of excitonic bound states that occur as a result of the long-range interactions.

cond-mat.str-el↗

arXiv2003

Renormalization Group and Decoupling in Curved Space

It is well known that the renormalization group equations depend on the scale where they are applied. This phenomenon is especially relevant for the massive fields in curved space, because the decoupling effects may be responsible for important cosmological applications like the graceful exit from the inflation and low-energy quantum dynamics of the cosmological constant. We investigate, using both covariant and non-covariant methods of calculations and mass-dependent renormalization scheme, the vacuum quantum effects of a massive scalar field in curved space-time. In the higher derivative sector we arrive at the explicit form of decoupling and obtain the beta-functions in both UV and IR regimes as the limits of general expressions. For the cosmological and Newton constants the corresponding beta-functions are not accessible in the perturbative regime and in particular the form of decoupling remains unclear.

hep-ph↗

arXiv2002

Magnetic field driven metal-insulator phase transition in planar systems

A theory of the magnetic field driven (semi-)metal-insulator 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 $B_c$, 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.

cond-mat↗

arXiv2001

Dynamical Chiral Symmetry Breaking on a Brane in Reduced QED

Reduced gauge theories are theories in which while gauge fields propagate in a bulk, fermion fields are localized on a brane. We study dynamical chiral symmetry breaking on a 2-brane and a 1-brane in reduced QED_{3+1}, and on a 1-brane in reduced QED_{2+1}. Since, unlike higher dimensional gauge theories, QED_{3+1} and QED_{2+1} are well defined, their reduced versions can serve as a laboratory for studying dynamics in a higher dimensional brane world. The analysis of the Schwinger-Dyson (SD) equations in these theories reveals rich and quite nontrivial dynamics in which the conformal symmetry and its breakdown play a crucial role. Explicit solutions of the SD equations in the near-critical regime are obtained and the character of the corresponding phase transition is described.

hep-ph↗

arXiv2000

On Chiral Symmetry Breaking in a Constant Magnetic Field in Higher Dimension

Chiral symmetry breaking in the Nambu-Jona-Lasinio model in a constant magnetic field is studied in spacetimes of dimension D > 4. It is shown that a constant magnetic field can be characterized by [(D-1)/2] parameters. For the maximal number of nonzero field parameters, we show that there is an effective reduction of the spacetime dimension for fermions in the infrared region D $\to$ 1 + 1 for even-dimensional spacetimes and D $\to$ 0 + 1 for odd-dimensional spacetimes. Explicit solutions of the gap equation confirm our conclusions.

hep-th↗

arXiv2000

On Color Superconductivity in External Magnetic Field

We study color superconductivity in external magnetic field. We discuss the reason why the mixing angles in color-flavor locked (CFL) and two-flavor superconductivity (2SC) phases are different despite the fact that the CFL gap goes to the 2SC gap for $m_s \to \infty$. Although flavor symmetry is explicitly broken in external magnetic field, we show that all values of gaps in their coset spaces of possible solutions in the CFL phase are equivalent in external magnetic field.

hep-ph↗

arXiv1999

Relating the Quark and Gluon Condensates Through the QCD Vacuum Energy

Using the Cornwall-Jackiw-Tomboulis effective potential for composite operators we compute the QCD vacuum energy as a function of the dynamical quark and gluon propagators, which are related to their respective condensates as predicted by the operator product expansion. The identification of this result to the vacuum energy obtained from the trace of the energy-momentum tensor allow us to study the gluon self-energy, verifying that it is fairly represented in the ultraviolet by the asymptotic behavior predicted by the operator product expansion, and in the infrared it is frozen at its asymptotic value at one scale of the order of the dynamical gluon mass. We also discuss the implications of this identity for heavy and light quarks. For heavy quarks we recover, through the vacuum energy calculation, the relation $m_{f} <{\bar{ψ_f}}ψ_f> \sim - {1/12} \gc$ obtained many years ago with QCD sum rules.

hep-ph↗