Nearly conformal gauge theories in finite volume

We report new results on nearly conformal gauge theories with fermions in the fundamental representation of the SU(3)$\mathit{SU}(3)$ color gauge group as the number of fermion flavors is varied in the Nf=4–16$N_f=4\text{–}16$ range. To unambiguously identify the chirally broken phase below the conformal window we apply a comprehensive lattice tool set in finite volumes which includes the test of Goldstone pion dynamics, the spectrum of the fermion Dirac operator, and eigenvalue distributions of random matrix theory. We also discuss the theory inside the conformal window and present our first results on the running of the renormalized gauge coupling and the renormalization group beta function. The importance of understanding finite volume zero momentum gauge field dynamics inside the conformal window is illustrated. Staggered lattice fermions are used throughout the calculations.     

Critical behavior of an anisotropic Ising antiferromagnet in both external longitudinal and transverse fields

In this paper we study the critical behavior of a two-sublattice Ising model on an anisotropic square lattice in both uniform longitudinal (H  ) and transverse (Ω$\Omega$) fields by using the effective-field theory. The model consists of ferromagnetic interaction J_x in the x direction and antiferromagnetic interaction J_y in the y direction in the presence of the H   and Ω$\Omega$ fields. We obtain the phase diagrams in the H–T$H–T$ and Ω–T$\Omega –T$ planes changing values of the Ω$\Omega$ and H   parameters, respectively for fixed value at λ=_Jx/_Jy=1$\lambda =J_x/J_y=1$. At null temperature, the ground state phase diagram in the Ω–H$\Omega –H$ plane for several values of λ$\lambda$ parameter is analyzed. In the particular case of λ=1$\lambda =1$ we compare our results with mean-field theory (MFT) and was not observed reentrant behavior around of the critical field _Hc/_Jy=2.0$H_c/J_y=2.0$ for Ω=0$\Omega =0$ by using EFT.     

Confined hidden vector dark matter

We argue that the lightest vector bound states of a confining hidden sector communicating with the Standard Model through the Higgs portal are stable and are viable candidates of dark matter. The model is based on an SU(2)$\mathit{SU}(2)$ gauge group with a scalar field in its fundamental representation and the stability of the lightest vector bound state results from the existence of a custodial symmetry. As the relic density depends essentially on the scale of confinement in the hidden sector, ΛHS${\Lambda }_{\mathrm{HS}}$, agreement with WMAP abundance requires ΛHS${\Lambda }_{\mathrm{HS}}$ in the 20–120 TeV range.     

Two-dimensional gauge theory and matrix model

We study a matrix model obtained by dimensionally reducing Chern–Simons theory on S³$S^3$. We find that the matrix integration is decomposed into sectors classified by the representation of SU(2)$\mathit{SU}(2)$. We show that the N  -block sectors reproduce SU(N)$\mathit{SU}(N)$ Yang–Mills theory on S²$S^2$ as the matrix size goes to infinity.     

Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization

The ultraviolet singular structure of the bulk-to-bulk propagators for higher spin gauge fields in AdS₄${\mathit{AdS}}_4$ space is analyzed in details. Possible interactions with the Higgs scalar and the corresponding one loop mass renormalization are studied. This mass renormalization is finite and connected with the anomalous dimensions of those currents in the corresponding boundary CFT₃${\mathit{CFT}}_3$ that cease to be conserved when the interaction is switched on. In particular it is proportional to ?−2$?-2$.     

Supersymmetric grand unification with light color-triplet

We construct a natural model of the supersymmetric SU(6)$\mathit{SU}(6)$ unification, in which the symmetry breaking, down to the standard model gauge group, results in the number of pseudo-Nambu–Goldstone superfields with interesting properties. Namely, besides the Higgs doublet–antidoublet pair which is responsible for the electroweak phase transition, the Nambu–Goldstone sector consists of multiplets in the anti- and fundamental representations of SU(5)$\mathit{SU}(5)$. While being strictly massless in the supersymmetric limit, they acquire the weak scale masses as a result of its breaking. The color-triplet components of this light sector could, in principle, mediate an unacceptably fast proton decay; however, because of the natural TeV/_MGUT$\text{TeV}/M_{\mathrm{GUT}}$ suppression of the Yukawa couplings to the light quarks and leptons, their existence is compatible with the experimental bound on proton lifetime. This suppression is made further interesting, since it results in the lifetime, of the lightest of the above-mentioned colored particles from 1 s to 1 day$1\text{day}$, long enough for it to appear stable in the detector. Furthermore, we argue that the accommodation of the color-triplet pseudo-Nambu–Goldstones, without fine-tuning or contradicting observations, implies SU(6)$\mathit{SU}(6)$ unification.     

Atomic parity violation in the economical 3–3–1 model

The deviation δQW$\delta Q_{\mathrm{W}}$ of the weak charge from its standard model prediction due to the mixing of the W boson with the charged bilepton Y as well as of the Z   boson with the neutral Z^′$Z^{\prime }$ and the real part of the non-Hermitian neutral bilepton X   in the economical 3–3–1 model is established. Additional contributions to the usual δQW$\delta Q_{\mathrm{W}}$ expression in the extra U(1)$\mathrm{U}(1)$ models and the left–right models are obtained. Our calculations are quite different from previous analyzes in this kind of the 3–3–1 models and give the limit on mass of the Z^′$Z^{\prime }$ boson, the Z–Z^′$Z\text{–}{Z}^{\prime }$ and W–Y$W\text{–}Y$ mixing angles with the more appropriate values: MZ^′>564 GeV$M_{Z^{\prime }}>564\text{GeV}$, −0.018<sinφ<0$-0.018<\sin \phi <0$ and |sinθ|<0.043$|\sin \theta |<0.043$.     

A six-dimensional gauge-Higgs unification model based on E6 gauge symmetry

We construct a six-dimensional gauge-Higgs unification model with the enlarged gauge group of E₆ on S²/Z₂$S^2/Z_2$ orbifold compactification. The standard model particle contents and gauge symmetry are obtained by utilizing a monopole background field and imposing appropriate parity conditions on the orbifold. In particular, a realistic Higgs potential suitable for breaking the electroweak gauge symmetry is obtained without introducing extra matter or assuming an additional symmetry relation between the SU(2) isometry transformation on the S²$S^2$ and the gauge symmetry. The Higgs boson is a KK mode associated with the extra-dimensional components of gauge field. We also compute the KK masses of all fields at tree level.     

Mini little Higgs and dark matter

We construct a little Higgs model with the most minimal extension of the standard model gauge group by an extra U(1)$U(1)$ gauge symmetry. For specific charge assignments of scalars, an approximate U(3)$U(3)$ global symmetry appears in the cutoff-squared scalar mass terms generated from gauge bosons at one-loop level. Hence, the Higgs boson, identified as a pseudo-Goldstone boson of the broken global symmetry, has its mass radiatively protected up to scales of 5–10 TeV. In this model, a Z₂$Z_2$ symmetry, ensuring the two U(1)$U(1)$ gauge groups to be identical, also makes the extra massive neutral gauge boson stable and a viable dark matter candidate with a promising prospect of direct detection.     

Hermitian–Einstein connections on polystable orthogonal and symplectic parabolic Higgs bundles

Let X$X$ be a smooth complex projective curve and S⊂X$S\subset X$ a finite subset. We show that an orthogonal or symplectic parabolic Higgs bundle on X$X$ with parabolic structure over S$S$ admits a Hermitian–Einstein connection if and only if it is polystable.     

General trilinear interaction for arbitrary even higher spin gauge fields

Using Noether's procedure we present a complete solution for the trilinear interactions of arbitrary spins s₁$s_1$, s₂$s_2$, s₃$s_3$ in a flat background, and discuss the possibility to enlarge this construction to higher order interactions in the gauge field. Some classification theorems of the cubic (self)interaction with different numbers of derivatives and depending on relations between the spins are presented. Finally the expansion of a general spin s gauge transformation into powers of the field and the related closure of the gauge algebra in the general case are discussed.     

Direct evidence for a Coulombic phase in monopole-suppressed SU(2) lattice gauge theory

Further evidence is presented for the existence of a non-confining phase at weak coupling in SU(2) lattice gauge theory. Using Monte Carlo simulations with the standard Wilson action, gauge-invariant SO(3)–Z2 monopoles, which are strong-coupling lattice artifacts, have been seen to undergo a percolation transition exactly at the phase transition previously seen using Coulomb gauge methods, with an infinite lattice critical point near β=3.2$\beta =3.2$. The theory with both Z2 vortices and monopoles and SO(3)–Z2 monopoles eliminated is simulated in the strong-coupling (β=0$\beta =0$) limit on lattices up to 60⁴. Here, as in the high-β phase of the Wilson-action theory, finite size scaling shows it spontaneously breaks the remnant symmetry left over after Coulomb gauge fixing. Such a symmetry breaking precludes the potential from having a linear term. The monopole restriction appears to prevent the transition to a confining phase at any β  . Direct measurement of the instantaneous Coulomb potential shows a Coulombic form with moderately running coupling possibly approaching an infrared fixed point of α∼1.4$\alpha \sim 1.4$. The Coulomb potential is measured to 50 lattice spacings and 2 fm. A short-distance fit to the 2-loop perturbative potential is used to set the scale. High precision at such long distances is made possible through the use of open boundary conditions, which was previously found to cut random and systematic errors of the Coulomb gauge fixing procedure dramatically. The Coulomb potential agrees with the gauge-invariant interquark potential measured with smeared Wilson loops on periodic lattices as far as the latter can be practically measured with similar statistics data.     

Z(2) gauge neural network and its phase structure

We study general phase structures of neural-network models that have Z(2) local gauge symmetry. The Z(2) spin variable _Si=±1$S_i=\pm 1$ on the i$i$-th site describes a neuron state as in the Hopfield model, and the Z(2) gauge variable _Jij=±1$J_{ij}=\pm 1$ describes a state of the synaptic connection between j$j$-th and i$i$-th neurons. The gauge symmetry allows for a self-coupling energy among _Jij$J_{ij}$’s such as _JijJjkJki$J_{ij}{J}_{jk}{J}_{ki}$, which describes reverberation of signals. Explicitly, we consider the three models; (I) an annealed model with full and partial connections of _Jij$J_{ij}$, (II) a quenched model with full connections where _Jij$J_{ij}$ is treated as a slow quenched variable, and (III) a quenched three-dimensional lattice model with the nearest-neighbor connections. By numerical simulations, we examine their phase structures paying attention to the effect of the reverberation term, and compare them with each other and with the annealed 3D lattice model which has been studied beforehand. By noting the dependence of thermodynamic quantities upon the total number of sites and the connectivity among sites, we obtain a coherent interpretation to understand these results. Among other things, we find that the Higgs phase of the annealed model is separated into two stable spin-glass phases in the quenched models (II) and (III).     

Effect of target density on YBCO thin films deposited from nanograined targets

Nanograined YBa₂Cu₃O_6+x${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{6+x}$ (YBCO) targets with grain sizes of 25–45 nm and different densities were prepared with sol–gel method. The properties of the thin films laser deposited from these targets were systematically studied. It was found that most parameters are not clearly affected by the target density, although the surface roughness decreased with target density. A small effect of decreasing J_c$J_{\text{c}}$ with increasing target density was observed, but this can be interpreted as film to film variation. On the other hand, a negative correlation between the accommodation field, B^∗$B^{\ast }$, and zero field J_c$J_{\text{c}}$ was observed and B^∗$B^{\ast }$ was found to increase with increasing number of lattice defects. Thus target density is found not to have a large effects on the superconducting or structural properties of YBCO thin films.     

Thermodynamics properties of an anisotropic Ising antiferromagnet in both external longitudinal and transverse fields

We have studied the anisotropic two-dimensional nearest-neighbor Ising model with competitive interactions in both uniform longitudinal field H$H$ and transverse magnetic field Ω$\Omega$. Using the effective-field theory (EFT) with correlation in cluster with N=1$N=1$ spin we calculate the thermodynamic properties as a function of temperature with values H$H$ and Ω$\Omega$ fixed. The model consists of ferromagnetic interaction _Jx$J_x$ in the x$x$ direction and antiferromagnetic interaction _Jy$J_y$ in the y$y$ direction, and it is found that for H/_Jy∈[0,2]$H/J_y\in [0,2]$ the system exhibits a second-order phase transition. The thermodynamic properties are obtained for the particular case of λ=_Jx/_Jy=1$\lambda =J_x/J_y=1$ (isotropic square lattice).     

Running inflation in the Standard Model

An interacting scalar field with largish coupling to curvature can support a distinctive inflationary universe scenario. Previously this has been discussed for the Standard Model Higgs field, treated classically or in a leading log approximation. Here we investigate the quantum theory using renormalization group methods. In this model the running of both the effective Planck mass and the couplings is important. The cosmological predictions are consistent with existing WMAP5 data, with 0.967?ns?0.98$0.967?n_s?0.98$ (for Ne=60$N_e=60$) and negligible gravity waves. We find a relationship between the spectral index and the Higgs mass that is sharply varying for mh∼120–135 GeV$m_h\sim 120\text{–}135\text{GeV}$ (depending on the top mass); in the future, that relationship could be tested against data from PLANCK and LHC. We also comment briefly on how similar dynamics might arise in more general settings, and discuss our assumptions from the effective field theory point of view.