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+13+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