A purely algebraic construction of a gauge and renormalization group invariant scalar glueball operator

This paper presents a complete algebraic proof of the renormalizability of the gauge invariant $d=4$ operator $F_{\mu\nu}^2(x)$ to all orders of perturbation theory in pure Yang-Mills gauge theory, whereby working in the Landau gauge. This renormalization is far from being trivial as mixing occurs with other $d=4$ gauge variant operators, which we identify explicitly. We determine the mixing matrix $Z$ to all orders in perturbation theory by using only algebraic arguments and consequently we can uncover a renormalization group invariant by using the anomalous dimension matrix $\Gamma$ derived from $Z$. We also present a future plan for calculating the mass of the lightest scalar glueball with the help of the framework we have set up.Comment: 17 page

A further study of the possible scaling region of lattice chiral fermions

In the possible scaling region for an SU(2) lattice chiral fermion advocated in {\it Nucl. Phys.} B486 (1997) 282, no hard spontaneous symmetry breaking occurs and doublers are gauge-invariantly decoupled via mixing with composite three-fermion-states that are formed by local multifermion interactions. However the strong coupling expansion breaks down due to no ``static limit'' for the low-energy limit ($pa\sim 0$). In both neutral and charged channels, we further analyze relevant truncated Green functions of three-fermion-operators by the strong coupling expansion and analytical continuation of these Green functions in the momentum space. It is shown that in the low-energy limit, these relevant truncated Green functions of three-fermion-states with the ``wrong'' chiralities positively vanish due to the generalized form factors (the wave-function renormalizations) of these composite three-fermion-states vanishing as O((pa)^4) for $pa\sim 0$. This strongly implies that the composite three-fermion-states with ``wrong'' chirality are ``decoupled'' in this limit and the low-energy spectrum is chiral, as a consequence, chiral gauge symmetries can be exactly preserved.Comment: A few typing-errors, in particular in Eq.50, have been correcte

Lattice gauge theory with baryons at strong coupling

We study the effective Hamiltonian for strong-coupling lattice QCD in the case of non-zero baryon density. In leading order the effective Hamiltonian is a generalized antiferromagnet. For naive fermions, the symmetry is U(4N_f) and the spins belong to a representation that depends on the local baryon number. Next-nearest-neighbor (nnn) terms in the Hamiltonian break the symmetry to U(N_f) x U(N_f). We transform the quantum problem to a Euclidean sigma model which we analyze in a 1/N_c expansion. In the vacuum sector we recover spontaneous breaking of chiral symmetry for the nearest-neighbor and nnn theories. For non-zero baryon density we study the nearest-neighbor theory only, and show that the pattern of spontaneous symmetry breaking depends on the baryon density.Comment: 31 pages, 5 EPS figures. Corrected Eq. (6.1

Oblique triangular antiferromagnetic phase in CsCu1−x_{1-x}Cox_xCl3_3

The spin-1/2 stacked triangular antiferromagnet CsCu$_{1-x}$Co$_x$Cl$_3$ with $0.015<x<0.032$ undergoes two phase transitions at zero field. The low-temperature phase is produced by the small amount of Co$^{2+}$ doping. In order to investigate the magnetic structures of the two ordered phases, the neutron elastic scattering experiments have been carried out for the sample with $x\approx 0.03$. It is found that the intermediate phase is identical to the ordered phase of CsCuCl$_3$, and that the low-temperature phase is an oblique triangular antiferromagnetic phase in which the spins form a triangular structure in a plane tilted from the basal plane. The tilting angle which is 42$^{\circ}$ at $T=1.6$ K decreases with increasing temperature, and becomes zero at $T_{\rm N2} =7.2$ K. An off-diagonal exchange term is proposed as the origin of the oblique phase.Comment: 6 pages, 7 figure

Holographic principle in the BDL brane cosmology

We study the holographic principle in the brane cosmology. Especially we describe how to accommodate the 5D anti de Sitter Schwarzschild (AdSS$_5$) black hole in the Binetruy-Deffayet-Langlois (BDL) approach of brane cosmology. It is easy to make a connection between a mass $M$ of the AdSS$_5$ black hole and a conformal field theory (CFT)-radiation dominated universe on the brane in the moving domain wall approach. But this is not established in the BDL approach. In this case we use two parameters $C_1, C_2$ in the Friedmann equation. These arise from integration and are really related to the choice of initial bulk matter. If one chooses a bulk energy density $\rho_B$ to account for a mass $M$ of the AdSS$_5$ black hole and the static fifth dimension, a CFT-radiation term with $\rho_{CFT} \sim M/a^{4}$ comes out from the bulk matter without introducing a localized matter distribution on the brane. This means that the holographic principle can be established in the BDL brane cosmology.Comment: 9 pages, a version to appear in PR

Glueballs, gluon condensate, and pure glue QCD below T_c

A quasiparticle description of pure glue QCD thermodynamics at T<T_c is proposed and compared to recent lattice data. Given that a gas of glueballs with constant mass cannot quantitatively reproduce the early stages of the deconfinement phase transition, the problem is to identify a relevant mechanism leading to the observed sudden increase of the pressure, trace anomaly, etc. It is shown that the strong decrease of the gluon condensate near T_c combined with the increasing thermal width of the lightest glueballs might be the trigger of the phase transition.Comment: 5 pages, 5 figures; analysis refined in v2, explanations added; v3 to appear in EPJ

Confront Holographic QCD with Regge Trajectories of vectors and axial-vectors

We derive the general 5-dimension metric structure of the $Dp-Dq$ system in type II superstring theory, and demonstrate the physical meaning of the parameters characterizing the 5-dimension metric structure of the \textit{holographic} QCD model by relating them to the parameters describing Regge trajectories. By matching the spectra of vector mesons $\rho_1$ with deformed $Dp-Dq$ soft-wall model, we find that the spectra of vector mesons $\rho_1$ can be described very well in the soft-wall $D3-Dq$ model, i.e, $AdS_5$ soft-wall model. We then investigate how well the $AdS_5$ soft-wall model can describe the Regge trajectory of axial-vector mesons $a_1$. We find that the constant component of the 5-dimension mass square of axial-vector mesons plays an efficient role to realize the chiral symmetry breaking in the vacuum, and a small negative $z^4$ correction in the 5-dimension mass square is helpful to realize the chiral symmetry restoration in high excitation states.Comment: 9 pages, 3 figure and 3 tables, one section adde

Spherically Symmetric Braneworld Solutions with R_{4} term in the Bulk

An analysis of a spherically symmetric braneworld configuration is performed when the intrinsic curvature scalar is included in the bulk action; the vanishing of the electric part of the Weyl tensor is used as the boundary condition for the embedding of the brane in the bulk. All the solutions outside a static localized matter distribution are found; some of them are of the Schwarzschild-(A)dS_{4} form. Two modified Oppenheimer-Volkoff interior solutions are also found; one is matched to a Schwarzschild-(A)dS_{4} exterior, while the other does not. A non-universal gravitational constant arises, depending on the density of the considered object; however, the conventional limits of the Newton's constant are recovered. An upper bound of the order of TeV for the energy string scale is extracted from the known solar system measurements (experiments). On the contrary, in usual brane dynamics, this string scale is calculated to be larger than TeV.Comment: 23 pages, 1 figure, one minor chang

Lorentz breaking Effective Field Theory and observational tests

Analogue models of gravity have provided an experimentally realizable test field for our ideas on quantum field theory in curved spacetimes but they have also inspired the investigation of possible departures from exact Lorentz invariance at microscopic scales. In this role they have joined, and sometime anticipated, several quantum gravity models characterized by Lorentz breaking phenomenology. A crucial difference between these speculations and other ones associated to quantum gravity scenarios, is the possibility to carry out observational and experimental tests which have nowadays led to a broad range of constraints on departures from Lorentz invariance. We shall review here the effective field theory approach to Lorentz breaking in the matter sector, present the constraints provided by the available observations and finally discuss the implications of the persisting uncertainty on the composition of the ultra high energy cosmic rays for the constraints on the higher order, analogue gravity inspired, Lorentz violations.Comment: 47 pages, 4 figures. Lecture Notes for the IX SIGRAV School on "Analogue Gravity", Como (Italy), May 2011. V.3. Typo corrected, references adde

Brane World Cosmology with Gauss-Bonnet Interaction

We study a Randall-Sundrum model modified by a Gauss-Bonnet interaction term. We consider, in particular, a Friedmann-Robertson-Walker metric on the brane and analyse the resulting cosmological scenario. It is shown that the usual Friedmann equations are recovered on the brane. The equation of state relating the enery density and the pressure is uniquely determined by the matching conditions. A cosmological solution with negative pressure is found.Comment: 9 pages, revtex styl