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.

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

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

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

Thermal conductivity and competing orders in d-wave superconductors

We derive the expression for the thermal conductivity \kappa in the low-temperature limit T \to 0 in d-wave superconductors, taking into account the presence of competing orders such as spin-density wave, is-pairing, etc.. The expression is used for analyzing recent experimental data in La_{2-x}Sr_xCuO_4. Our analysis strongly suggests that competing orders can be responsible for anomalies in behavior of thermal conductivity observed in those experiments.Comment: revtex4,6 pages,title changed,references and two eps figures added,text essentially extended,to appear in EPJ

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 $SU(2)\times U(1)_Y$ $\sigma$-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.Comment: Revtex, 13 pages, 4 figures, v2: to match PRD versio

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

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.Comment: 19 pages, REVTeX4, v2: clarifications added, v3: to match PRD versio