108 research outputs found

### Cornwall-Jackiw-Tomboulis effective potential for quark propagator in real-time thermal field theory and Landau gauge

We complete the derivation of the Cornwall-Jackiw-Tomboulis effective
potential for quark propagator at finite temperature and finite quark chemical
potential in the real-time formalism of thermal field theory and in Landau
gauge. In the approximation that the function $A(p^2)$ in inverse quark
propagator is replaced by unity, by means of the running gauge coupling and the
quark mass function invariant under the renormalization group in zero
temperature Quantum Chromadynamics (QCD), we obtain a calculable expression for
the thermal effective potential which will be a useful means to research chiral
phase transition in QCD in the real-time formalism.Comment: 5 pages, Latex, no figur

### The effective potential of composite diquark fields and the spectrum of resonances in dense QCD

The effective potential of composite diquark fields responsible for color
symmetry breaking in cold very dense QCD, in which long-range interactions
dominate, is derived. The spectrum of excitations and the universality class of
this dynamics are described.Comment: 8 pages, 1 figure (new), REVTeX. The latest version to appear in
Phys. Lett. B. References added, discussion improve

### Dynamical chiral symmetry breaking in gauge theories with extra dimensions

We investigate dynamical chiral symmetry breaking in vector-like gauge
theories in $D$ dimensions with ($D-4$) compactified extra dimensions, based on
the gap equation (Schwinger-Dyson equation) and the effective potential for the
bulk gauge theories within the improved ladder approximation. The non-local
gauge fixing method is adopted so as to keep the ladder approximation
consistent with the Ward-Takahashi identities.
Using the one-loop $\bar{\rm MS}$ gauge coupling of the truncated KK
effective theory which has a nontrivial ultraviolet fixed point (UV-FP) $g_*$
for the (dimensionless) bulk gauge coupling ${\hat g}$, we find that there
exists a critical number of flavors, $N_f^{\rm crit}$ ($\simeq 4.2, 1.8$ for
$D=6, 8$ for SU(3) gauge theory): For $N_f > N_f^{\rm crit}$, the dynamical
chiral symmetry breaking takes place not only in the ``strong-coupling phase''
(${\hat g} >g_*$) but also in the ``weak-coupling phase'' (${\hat g} <g_*$)
when the cutoff is large enough. For $N_f < N_f^{\rm crit}$, on the other hand,
only the strong-coupling phase is a broken phase and we can formally define a
continuum (infinite cutoff) limit, so that the physics is insensitive to the
cutoff in this case.
We also perform a similar analysis using the one-loop ``effective gauge
coupling''. We find the $N_f^{\rm crit}$ turns out to be a value similar to
that of the $\bar{\rm MS}$ case, notwithstanding the enhancement of the
coupling compared with that of the $\bar{\rm MS}$.Comment: REVTEX4, 38 pages, 18 figures. The abstract is shortened; version to
be published in Phys. Rev.

### Conformal phase transition: QCD like theories with a large number of fermion flavors and all that

The notion of the conformal phase transiton (CPhT) is discussed. As its realization, the dynamics with an infrared stable fixed point in the conformal window in QCD like theories with a relatively large number of fermion flavors is reviewed. The emphasis is on the description of a clear signature for the conformal window, which in particular can be useful for lattice computer simulations of these gauge theories. A possibility of the relevance of the CPhT in graphene is mentioned

### Dimensional Reduction and Dynamical Chiral Symmetry Breaking by a Magnetic Field in $3+1$ Dimensions

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 $D \rightarrow D-2$ ($3+1 \rightarrow
1+1$) 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.Comment: 13 pages, LaTeX, no figure

### Electrical Neutrality and Symmetry Restoring Phase Transitions at High Density in a Two-Flavor Nambu-Jona-Lasinio Model

A general research on chiral symmetry restoring phase transitions at zero
temperature and finite chemical potentials under electrical neutrality
condition has been conducted in a Nambu-Jona-Lasinio model to describe
two-flavor normal quark matter. Depending on that $m_0/\Lambda$, the ratio of
dynamical quark mass in vacuum and the 3D momentum cutoff in the loop
integrals, is less or greater than 0.413, the phase transition will be second
or first order. A complete phase diagram of $u$ quark chemical potential versus
$m_0$ is given. With the electrical neutrality constraint, the region where
second order phase transition happens will be wider than the one without
electrical neutrality limitation. The results also show that, for the value of
$m_0/\Lambda$ from QCD phenomenology, the phase transition must be first order.Comment: 9 pages, 1 figur

### Dynamical stabilization of runaway potentials at finite density

We study four dimensional non-abelian gauge theories with classical moduli.
Introducing a chemical potential for a flavor charge causes moduli to become
unstable and start condensing. We show that the moduli condensation in the
presence of a chemical potential generates nonabelian field strength
condensates. These condensates are homogeneous but non-isotropic. The end point
of the condensation process is a stable homogeneous, but non-isotropic, vacuum
in which both gauge and flavor symmetries and the rotational invariance are
spontaneously broken. Possible applications of this phenomenon for the gauge
theory/string theory correspondence and in cosmology are briefly discussed.Comment: revtex4, 4 pages; v.2: journal versio

### Longitudinal gluons and Nambu-Goldstone bosons in a two-flavor color superconductor

In a two-flavor color superconductor, the SU(3)_c gauge symmetry is
spontaneously broken by diquark condensation. The Nambu-Goldstone excitations
of the diquark condensate mix with the gluons associated with the broken
generators of the original gauge group. It is shown how one can decouple these
modes with a particular choice of 't Hooft gauge. We then explicitly compute
the spectral density for transverse and longitudinal gluons of adjoint color 8.
The Nambu-Goldstone excitations give rise to a singularity in the real part of
the longitudinal gluon self-energy. This leads to a vanishing gluon spectral
density for energies and momenta located on the dispersion branch of the
Nambu-Goldstone excitations.Comment: 16 pages, 4 figures, minor revisions to text, one ref. adde

### Toward theory of quantum Hall effect in graphene

We analyze a gap equation for the propagator of Dirac quasiparticles and conclude that in graphene in a
magnetic field, the order parameters connected with the quantum Hall ferromagnetism dynamics and those
connected with the magnetic catalysis dynamics necessarily coexist (the latter have the form of Dirac masses
and correspond to excitonic condensates). This feature of graphene could lead to important consequences, in
particular, for the existence of gapless edge states. Solutions of the gap equation corresponding to recently
experimentally discovered novel plateaus in graphene in strong magnetic fields are described

### Quark-Antiquark and Diquark Condensates in Vacuum in a 2D Two-Flavor Gross-Neveu Model

The analysis based on the renormalized effective potential indicates that,
similar to in the 4D two-flavor Nambu-Jona-Lasinio (NJL) model, in a 2D
two-flavor Gross-Neveu model, the interplay between the quark-antiquark and the
diquark condensates in vacuum also depends on $G_S/H_S$, the ratio of the
coupling constants in scalar quark-antiquark and scalar diquark channel. Only
the pure quark-antiquark condensates exist if $G_S/H_S>2/3$ which is just the
ratio of the color numbers of the quarks participating in the diquark and
quark-antiquark condensates. The two condensates will coexist if
$0<G_S/H_S<2/3$. However, different from the 4D NJL model, the pure diquark
condensates arise only at $G_S/H_S=0$ and are not in a possibly finite region
of $G_S/H_S$ below 2/3.Comment: 6 pages, revtex4, no figur

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