Conformal phase transition in QCD like theories and beyond

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.Comment: 10 pages, 1 figure, Talk at Workshop on Strong Coupling Gauge Theories in the LHC Era, December 8-11, 2009, Nagoya, Japa

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

Dynamics of QCD in a Strong Magnetic Field

QCD in a strong magnetic field yields an example of a rich, sophisticated and controllable dynamics.Comment: 12 pages, 1 figure, Latex, Talk at Symposium and Workshop "Continuous Advances in QCD 2002/Arkadyfest, May 17-23, 200

Techni-dilaton at Conformal Edge

Techni-dilaton (TD) was proposed long ago in the technicolor (TC) near criticality/conformality. To reveal the critical behavior of TD, we explicitly compute the nonperturbative contributions to the scale anomaly $$and to the techni-gluon condensate$$, which are generated by the dynamical mass m of the techni-fermions. Our computation is based on the (improved) ladder Schwinger-Dyson equation, with the gauge coupling $\alpha$ replaced by the two-loop running one $\alpha(\mu)$ having the Caswell-Banks-Zaks IR fixed point $\alpha_*$: $\alpha(\mu) \simeq \alpha = \alpha_*$ for the IR region $m < \mu < \Lambda_{TC}$, where $\Lambda_{TC}$ is the intrinsic scale (analogue of $\Lambda_{QCD}$ of QCD) relevant to the perturbative scale anomaly. We find that $-/m^4\to const \ne 0$ and $/m^4\to (\alpha/\alpha_{cr}-1)^{-3/2}\to\infty$ in the criticality limit $m/\Lambda_{TC}\sim\exp(-\pi/(\alpha/\alpha_{cr}-1)^{1/2})\to 0$ ($\alpha=\alpha_* \to \alpha_{cr}$) ("conformal edge"). Our result precisely reproduces the formal identity $=(\beta(\alpha)/4 \alpha)$, where $\beta(\alpha)=-(2\alpha_{cr}/\pi) (\alpha/\alpha_{cr}-1)^{3/2}$ is the nonperturbative beta function corresponding to the above essential singularity scaling of $m/\Lambda_{TC}$. Accordingly, the PCDC implies $(M_{TD}/m)^2 (F_{TD}/m)^2=-4/m^4 \to const \ne 0$ at criticality limit, where $M_{TD}$ is the mass of TD and $F_{TD}$ the decay constant of TD. We thus conclude that at criticality limit the TD could become a "true (massless) Nambu-Goldstone boson" $M_{TD}/m\to 0$, only when $m/F_{TD}\to 0$, namely getting decoupled, as was the case of "holographic TD" of Haba-Matsuzaki-Yamawaki. The decoupled TD can be a candidate of dark matter.Comment: 17 pages, 14 figures; discussions clarified, references added, to appear in Phys.Rev.

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.Comment: 5 pages, no figures, v.2: to match published versio

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

A study of Schwinger-Dyson Equations for Yukawa and Wess-Zumino Models

We study Schwinger-Dyson equation for fermions in Yukawa and Wess-Zumino models, in terms of dynamical mass generation and the wavefunction renormalization function. In the Yukawa model with $\gamma_5$-type interaction between scalars and fermions, we find a critical coupling in the quenched approximation above which fermions acquire dynamical mass. This is shown to be true beyond the bare 3-point vertex approximation. In the Wess-Zumino model, there is a neat cancellation of terms leading to no dynamical mass for fermions. We comment on the conditions under which these results are general beyond the rainbow approximation and also on the ones under which supersymmetry is preserved and the scalars as well do not acquire mass. The results are in accordance with the non-renormalization theorem at least to order $\alpha$ in perturbation theory. In both the models, we also evaluate the wavefunction renormalization function, analytically in the neighbourhood of the critical coupling and numerically, away from it.Comment: 12 pages and 7 Postscript figures, accepted for publication in Journal of Physics G: Nuclear and Particle Physic