Perturbative Thermodynamics of Lattice QCD with Chiral-Invariant Four-Fermion Interactions

Lattice QCD with additional chiral-invariant four-fermion interactions is studied at nonzero temperature. Staggered Kogut-Susskind quarks are used. The four-fermion interactions are implemented by introducing bosonic auxiliary fields. A mean field treatment of the auxiliary fields is used to calculate the model's asymptotic scale parameter and perturbative thermodynamics, including the one-loop gluonic contributions to the energy, entropy, and pressure. In this approach the calculations reduce to those of ordinary lattice QCD with massive quarks. Hence, the previous calculations of these quantities in lattice QCD using massless quarks are generalized to the massive case.Comment: 22 pages, RevTeX, 8 EPS figures, uses epsf.sty and feynmf.st

The beta function and equation of state for QCD with two flavors of quarks

We measure the pressure and energy density of two flavor QCD in a wide range of quark masses and temperatures. The pressure is obtained from an integral over the average plaquette or psi-bar-psi. We measure the QCD beta function, including the anomalous dimension of the quark mass, in new Monte Carlo simulations and from results in the literature. We use it to find the interaction measure, E-3p, yielding non-perturbative values for both the energy density E and the pressure p. uuencoded compressed PostScript file Revised version should work on more PostScript printers.Comment: 24 page

The pressure of strong coupling lattice QCD with heavy quarks, the hadron resonance gas model and the large N limit

In this paper we calculate the pressure of pure lattice Yang-Mills theories and lattice QCD with heavy quarks by means of strong coupling expansions. Dynamical fermions are introduced with a hopping parameter expansion, which also allows for the incorporation of finite quark chemical potential. We show that in leading orders the results are in full agreement with expectations from the hadron resonance gas model, thus validating it with a first principles calculation. For pure Yang-Mills theories we obtain the corresponding ideal glueball gas, in QCD with heavy quarks our result equals that of an ideal gas of mesons and baryons. Another finding is that the Yang-Mills pressure in the large N limit is of order $\sim N^0$ to the calculated orders, when the inverse 't Hooft coupling is used as expansion parameter. This property is expected in the confined phase, where our calculations take place.Comment: 12 pages, 4 figure

Lattice sum rules for the colour fields

We analyse the sum rules describing the action and energy in the colour fields around glueballs, torelons and static potentials.Comment: 9 pages LATEX, (typos corrected, to appear in Phys Rev D

Some Applications of Thermal Field Theory to Quark-Gluon Plasma

The lecture provides a brief introduction of thermal field theory within imaginary time formalism, the Hard Thermal Loop perturbation theory and some of its application to the physics of the quark-gluon plasma, possibly created in relativistic heavy ion collisions.Comment: 17 pages, 12 figures : Lectures given in "Workshop on Hadron Physics" during March 7-17, 2005, Puri, Indi

The Rest-Frame Instant Form of Relativistic Perfect Fluids and of Non-Dissipative Elastic Materials

For perfect fluids with equation of state $\rho = \rho (n,s)$, Brown gave an action principle depending only on their Lagrange coordinates $\alpha^i(x)$ without Clebsch potentials. After a reformulation on arbitrary spacelike hypersurfaces in Minkowski spacetime, the Wigner-covariant rest-frame instant form of these perfect fluids is given. Their Hamiltonian invariant mass can be given in closed form for the dust and the photon gas. The action for the coupling to tetrad gravity is given. Dixon's multipoles for the perfect fluids are studied on the rest-frame Wigner hyperplane. It is also shown that the same formalism can be applied to non-dissipative relativistic elastic materials described in terms of Lagrangian coordinates.Comment: revtex file, 70 page

Elaborations on the String Dual to N=1 SQCD

In this paper we make further refinements to the duality proposed between N=1 SQCD and certain string (supergravity plus branes) backgrounds, working in the regime of comparable large number of colors and flavors. Using the string theory solutions, we predict different field theory observables and phenomena like Seiberg duality, gauge coupling and its running, the behavior of Wilson and 't Hooft loops, anomalous dimensions of the quark superfields, quartic superpotential coupling and its running, continuous and discrete anomaly matching. We also give evidence for the smooth interpolation between higgsed and confining vacua. We provide several matchings between field theory and string theory computations.Comment: 44 pages, 6 figures. References added, minor rewritings, published versio

The equation of state for two flavor QCD at N_t=6

We calculate the two flavor equation of state for QCD on lattices with lattice spacing a=(6T)^{-1} and find that cutoff effects are substantially reduced compared to an earlier study using a=(4T)^{-1}. However, it is likely that significant cutoff effects remain. We fit the lattice data to expected forms of the free energy density for a second order phase transition at zero-quark-mass, which allows us to extrapolate the equation of state to m_q=0 and to extract the speed of sound. We find that the equation of state depends weakly on the quark mass for small quark mass.Comment: 24 pages, latex, 11 postscipt figure

Non-perturbative determination of anisotropy coefficients in lattice gauge theories

We propose a new non-perturbative method to compute derivatives of gauge coupling constants with respect to anisotropic lattice spacings (anisotropy coefficients), which are required in an evaluation of thermodynamic quantities from numerical simulations on the lattice. Our method is based on a precise measurement of the finite temperature deconfining transition curve in the lattice coupling parameter space extended to anisotropic lattices by applying the spectral density method. We test the method for the cases of SU(2) and SU(3) gauge theories at the deconfining transition point on lattices with the lattice size in the time direction $N_t=4$ -- 6. In both cases, there is a clear discrepancy between our results and perturbative values. A longstanding problem, when one uses the perturbative anisotropy coefficients, is a non-vanishing pressure gap at the deconfining transition point in the SU(3) gauge theory. Using our non-perturbative anisotropy coefficients, we find that this problem is completely resolved: we obtain $\Delta p/T^4 = 0.001(15)$ and $-0.003(17)$ on $N_t=4$ and 6 lattices, respectively.Comment: 24pages,7figures,5table

Quarkonium Suppression

I discuss quarkonium suppression in equilibriated strongly interacting matter. After a brief review of basic features of quarkonium production I discuss the application of recent lattice data on the heavy quark potential to the problem of quarkonium dissociation as well as the problem of direct lattice determination of quarkonium properties in finite temperature lattice QCD.Comment: Invited plenary talk presented on 4th International Conference on Physics and Astrophysics of Quark Gluon Plasma (ICPAQGP-2001), November 26-30, 2001, Jaipur; 12 pp, LaTeX, uses pramana.st