QCD Pressure at Two Loops in the Temporal Gauge

We apply the method of \underline{zeta} functions, together with the $n_\mu^*$-prescription for the temporal gauge, to evaluate the thermodynamic pressure in QCD at finite temperature $T$. Working in the imaginary-time formalism and employing a special version of the unified-gauge prescription, we show that the pure-gauge contribution to the pressure at two loops is given by P_2^{\mbox{{\scriptsize gauge}}} = -(g^2/144)N_cN_gT^4, where $N_c$ and $N_g$ denote the number of colours and gluons, respectively. This result agrees with the value in the Feynman gauge.Comment: 19 pages, 2 figures, list of 63 integral

Explicit Construction of Yang-Mills Instantons on ALE Spaces

We describe the explicit construction of Yang-Mills instantons on ALE spaces, following the work of Kronheimer and Nakajima. For multicenter ALE metrics, we determine the abelian instanton connections which are needed for the construction in the non-abelian case. We compute the partition function of Maxwell theories on ALE manifolds and comment on the issue of electromagnetic duality. We discuss the topological characterization of the instanton bundles as well as the identification of their moduli spaces. We generalize the 't Hooft ansatz to SU(2) instantons on ALE spaces and on other hyper-Kahler manifolds. Specializing to the Eguchi-Hanson gravitational background, we explicitly solve the ADHM equations for SU(2) gauge bundles with second Chern class 1/2, 1 and 3/2.Comment: 59 pages, epsf.tex, 2 figures included, uuencoded fil

Sphalerons, instantons, and standing waves on S3⊗RS^3 \otimes R

We consider pure $SU(2)$ Yang-Mills theory when the space is compactified to a 3-dimensional sphere with finite radius. The Euclidean classical self-dual solutions of the equations of motion (the instantons) and the static finite energy solutions (the sphalerons) which have been found earlier are rewritten in handy physical variables with the gauge condition $A_0 = 0$. Stationary solutions to the equations of motion in the Minkowski space-time (the standing waves) are discussed. We briefly discuss also the theory defined in a flat finite spherical box with rigid boundary conditions and present the numerical solution describing the sphaleron.Comment: LaTeX, 16 pages, 2 figures in a separate uuencoded file. Minor Stylistic revision

Fractional Branes, Confinement, and Dynamically Generated Superpotentials

We examine the effects of instantons in four dimensional N=1 supersymmetric gauge theory by including D0-branes in type IIA brane constructions. We examine instanton generated superpotentials in supersymmetric QCD and find that they are due to a repulsive force between D4-branes bound to D0-branes ending on NS 5-branes. We study situations where instanton effects break supersymmetry such as the Intriligator-Thomas-Izawa-Yangagida model and relate this to a IIA brane construction. We also argue how confinement due to a condensate of fractional instantons manifests itself in Super Yang-Mills theory using fractional D0 branes, D4 branes, and NS strings.Comment: 19 pages, 2 figures, uses harvmac. References adde

First Order Variational Calculation of Form Factor in a Scalar Nucleon--Meson Theory

We investigate a relativistic quantum field theory in the particle representation using a non-perturbative variational technique. The theory is that of two massive scalar particles, `nucleons' and `mesons', interacting via a Yukawa coupling. We calculate the general Euclidean Green function involving two external nucleons and an arbitrary number of external mesons in the quenched approximation for the nucleons. The non-perturbative renormalization and truncation is done in a consistent manner and results in the same variational functional independent of the number of external mesons. We check that the calculation agrees with one-loop perturbation theory for small couplings. As an illustration the special case of meson absorption on the nucleon is considered in detail. We derive the radius of the dressed particle and numerically investigate the vertex function after analytic continuation to Minkowski space.Comment: 28 pages standard LaTeX, 13 uuencoded postscript figures embedded with psfig.st

Energy-Momentum Tensors for the Quark-Gluon Plasma

We construct the energy-momentum tensor for the gauge fields which describe the collective excitations of the quark-gluon plasma. We rely on the description of the collective modes that we have derived in previous works. By using the conservation laws for energy and momentum, we obtain three different versions for the tensor $T^{\mu\nu}$, which are physically equivalent. We show that the total energy constructed from $T^{00}$ is positive for any non-trivial field configuration. Finally, we present a new non-abelian solution of the equations of motion for the gauge fields. This solution corresponds to spatially uniform color oscillations of the plasma.Comment: 28 pages LaTex, Saclay preprint T94/0

The Polyakov loop and the heat kernel expansion at finite temperature

The lower order terms of the heat kernel expansion at coincident points are computed in the context of finite temperature quantum field theory for flat space-time and in the presence of general gauge and scalar fields which may be non Abelian and non stationary. The computation is carried out in the imaginary time formalism and the result is fully consistent with invariance under topologically large and small gauge transformations. The Polyakov loop is shown to play a fundamental role.Comment: 4 pages, REVTEX, no figure

Quark model description of quasi-elastic pion knockout from the proton at JLAB

The interference term between s- and t-pole contributions to the p(e,e' pi+)n cross section is evaluated on the basis of the constituent quark model. It is shown that the contribution of baryon s-poles can be modeled by a nonlocal extension of the Kroll-Rudermann contact term. This contribution is in a destructive interference with the pion t-pole that is essential to improve the description of recent JLab data at the invariant mass W=1.95 GeV. Some predictions are made for a new JLab measurement at higher values W=2.1-2.3 GeV and Q2 centered at 1.6 and 2.45 GeV2/c2.Comment: 15 pages, 4 figures, to be published in Phys. Lett.

Confinement and chiral condensates in 2-d QED with massive N-flavor fermions

We evaluate Polyakov loops and string tension in two-dimensional QED with both massless and massive $N$-flavor fermions at zero and finite temperature. External charges, or external electric fields, induce phases in fermion masses and shift the value of the vacuum angle parameter $\theta$, which in turn alters the chiral condensate. In particular, in the presence of two sources of opposite charges, $q$ and $-q$, the shift in $\theta$ is $2\pi(q/e)$ independent of $N$. The string tension has a cusp singularity at $\theta=\pm\pi$ for $N\ge 2$ and is proportional to $m^{2N/(N+1)}$ at $T=0$.Comment: 14 pages. LaTex + 2 postscript figures, uses epsf.st