Structure of the Electric Flux in N=4 Supersymmetric Yang-Mills Theory

Correlators of Wilson loop operators with O_4=Tr(F_{\mu\nu}^2+...) are computed in N=4 super-Yang-Mills theory using the AdS/CFT correspondence. The results are compared with the leading order perturbative computations. As a consequence of conformal invariance, these correlators have identical forms in the weak and strong coupling limits for circular loops. They are essentially different for contours not protected by conformal symmetry.Comment: 7 pages, 1 postscript figure, minor corrections and clarifying argument

Adjoint non-Abelian Coulomb gas at large N

The non-Abelian analog of the classical Coulomb gas is discussed. The statistical mechanics of arrays of classical particles which transform under various representations of a non-Abelian gauge group and which interact through non-Abelian electric fields are considered. The problem is formulated on the lattice and, for the case of adjoint charges, it is solved in the large N limit. The explicit solution exhibits a first order confinement-de-confinement phase transition with computable properties. In one dimension, the solution has a continuum limit which describes 1+1-dimensional quantum chromodynamics (QCD) with heavy adjoint matter.Comment: 21 pages, LaTe

Nonabelian D-branes and Noncommutative Geometry

We discuss the nonabelian world-volume action which governs the dynamics of N coincident Dp-branes. In this theory, the branes' transverse displacements are described by matrix-valued scalar fields, and so this is a natural physical framework for the appearance of noncommutative geometry. One example is the dielectric effect by which Dp-branes may be polarized into a noncommutative geometry by external fields. Another example is the appearance of noncommutative geometries in the description of intersecting D-branes of differing dimensions, such as D-strings ending on a D3- or D5-brane. We also describe the related physics of giant gravitons.Comment: 21 pages, Latex, ref. adde

Wilson Loops in N=4 Supersymmetric Yang--Mills Theory

Perturbative computations of the expectation value of the Wilson loop in N=4 supersymmetric Yang-Mills theory are reported. For the two special cases of a circular loop and a pair of anti-parallel lines, it is shown that the sum of an infinite class of ladder-like planar diagrams, when extrapolated to strong coupling, produces an expectation value characteristic of the results of the AdS/CFT correspondence, $\sim\exp((constant)\sqrt{g^2N})$. For the case of the circular loop, the sum is obtained analytically for all values of the coupling. In this case, the constant factor in front of $\sqrt{g^2N}$ also agrees with the supergravity results. We speculate that the sum of diagrams without internal vertices is exact and support this conjecture by showing that the leading corrections to the ladder diagrams cancel identically in four dimensions. We also show that, for arbitrary smooth loops, the ultraviolet divergences cancel to order $g^4N^2$.Comment: 24 pages, LaTeX, uses feynmp, 12 postscript figure

Deconfinement Transition for Quarks on a Line

We examine the statistical mechanics of a 1-dimensional gas of both adjoint and fundamental representation quarks which interact with each other through 1+1-dimensional U(N) gauge fields. Using large-N expansion we show that, when the density of fundamental quarks is small, there is a first order phase transition at a critical temperature and adjoint quark density which can be interpreted as deconfinement. When the fundamental quark density is comparable to the adjoint quark density, the phase transition becomes a third order one. We formulate a way to distinguish the phases by considering the expectation values of high winding number Polyakov loop operators.Comment: Reported problems with figures fixed; 38 pages, LaTeX, 5 figures, epsfi

Solitons on Branes

We examine the possibility that gauge field configurations on stacks of parallel Dp branes support topological solitons. We give an exhaustive list of possible soliton charges for p<7. We also discuss how configurations carrying the soliton charges can be constructed from intersecting branes.Comment: 15 pages, 2 figures; v2: two references added, version to be published in Nucl.Phys.

Longitudinal gluons and Nambu-Goldstone bosons in a two-flavor color superconductor

In a two-flavor color superconductor, the SU(3)_c gauge symmetry is spontaneously broken by diquark condensation. The Nambu-Goldstone excitations of the diquark condensate mix with the gluons associated with the broken generators of the original gauge group. It is shown how one can decouple these modes with a particular choice of 't Hooft gauge. We then explicitly compute the spectral density for transverse and longitudinal gluons of adjoint color 8. The Nambu-Goldstone excitations give rise to a singularity in the real part of the longitudinal gluon self-energy. This leads to a vanishing gluon spectral density for energies and momenta located on the dispersion branch of the Nambu-Goldstone excitations.Comment: 16 pages, 4 figures, minor revisions to text, one ref. adde

Fluctuation modes in color-superconductors

We investigate fluctuation effects of a gap parameter in color-superconductors. The fluctuation modes in the super phase are described by two scalar fields of diquarks. One of them is a Nambu-Goldstone boson and the other is a diquark boson whose mass is about twice of the gap energy (an extended quasi-supersymmetry). In the normal phase the fluctuation becomes a precursory (soft) mode whose amplitude increases near the critical temperature.Comment: 6 page

Magnetic catalysis and anisotropic confinement in QCD

The expressions for dynamical masses of quarks in the chiral limit in QCD in a strong magnetic field are obtained. A low energy effective action for the corresponding Nambu-Goldstone bosons is derived and the values of their decay constants as well as the velocities are calculated. The existence of a threshold value of the number of colors $N^{thr}_c$, dividing the theories with essentially different dynamics, is established. For the number of colors $N_c \ll N^{thr}_c$, an anisotropic dynamics of confinement with the confinement scale much less than $\Lambda_{QCD}$ and a rich spectrum of light glueballs is realized. For $N_c$ of order $N^{thr}_c$ or larger, a conventional confinement dynamics takes place. It is found that the threshold value $N^{thr}_c$ grows rapidly with the magnetic field [$N^{thr}_c \gtrsim 100$ for $|eB| \gtrsim (1{GeV})^2$]. In contrast to QCD with a nonzero baryon density, there are no principal obstacles for checking these results and predictions in lattice computer simulations.Comment: 10 pages, 1 figure. REVTeX. Minor correction. To appear in Phys. Rev.

Instanton Effects in QCD at High Baryon Density

We study instanton effects in QCD at very high baryon density. In this regime instantons are suppressed by a large power of $(\Lambda_{QCD}/\mu)$, where $\Lambda_{QCD}$ is the QCD scale parameter and $\mu$ is the baryon chemical potential. Instantons are nevertheless important because they contribute to several physical observables that vanish to all orders in perturbative QCD. We study, in particular, the chiral condensate and its contribution $m_{GB}^2\sim m$ to the masses of Goldstone bosons in the CFL phase of QCD with $N_f=3$ flavors. We find that at densities $\rho\sim (5-10) \rho_0$, where $\rho_0$ is the density of nuclear matter, the result is dominated by large instantons and subject to considerable uncertainties. We suggest that these uncertainties can be addressed using lattice calculations of the instanton density and the pseudoscalar diquark mass in QCD with two colors. We study the topological susceptibility and Witten-Veneziano type mass relations in both $N_c=2$ and $N_c=3$ QCD.Comment: 27 pages, 8 figures, minor revision