Gauge Fields and Space-Time

In this article I attempt to collect some ideas,opinions and formulae which may be useful in solving the problem of gauge/ string / space-time correspondence This includes the validity of D-brane representation, counting of gauge-invariant words, relations between the null states and the Yang-Mills equations and the discussion of the strong coupling limit of the string sigma model. The article is based on the talk given at the "Odyssey 2001" conference.Comment: 20 page

The Theory of Turbulence in Two Dimensions

The methods of conformal field theory are used to obtain the series of exact solutions of the fundamental equations of the theory of turbulence. The basic conjecture, proved to be self-consistent ,is the conformal invariance of the inertial range. The resulting physical picture is different from the standard one , since the enstrophy transfer is catalyzed by the large scale motions. The theory gives some unambiguous predictions for the correlations in the inertial range.Comment: 18 pages (Plain LateX), PUPT - 136

Monopoles and flux strings from SU(2) adjoint scalars

We construct, in an SU(2) gauge theory with two adjoint scalars, flux strings with monopoles attached at the ends. One scalar breaks SU(2) to U(1) and produces monopoles, the other then breaks the U(1) and produces strings. Dualizing, we write the theory in terms of effective string variables and show that the flux in the string is exactly saturated by the monopoles at the ends.Comment: 12 pp. v2: added several references and reworded some statement

Gauge Theory Correlators from Non-Critical String Theory

We suggest a means of obtaining certain Green's functions in 3+1-dimensional ${\cal N} = 4$ supersymmetric Yang-Mills theory with a large number of colors via non-critical string theory. The non-critical string theory is related to critical string theory in anti-deSitter background. We introduce a boundary of the anti-deSitter space analogous to a cut-off on the Liouville coordinate of the two-dimensional string theory. Correlation functions of operators in the gauge theory are related to the dependence of the supergravity action on the boundary conditions. From the quadratic terms in supergravity we read off the anomalous dimensions. For operators that couple to massless string states it has been established through absorption calculations that the anomalous dimensions vanish, and we rederive this result. The operators that couple to massive string states at level $n$ acquire anomalous dimensions that grow as 2\left (n g_{YM} \sqrt {2 N} )^{1/2} for large `t Hooft coupling. This is a new prediction about the strong coupling behavior of large $N$ SYM theory.Comment: 15 pages, harvmac with btxmac; minor revisions, 1 reference added, the version to appear in Physics Letters

Loop scattering in two-dimensional QCD

Using the integrability conditions that we recently obtained in QCD$_2$ with massless fermions, we arrive at a sufficient number of conservation laws to be able to fix the scattering amplitudes involving a local version of the Wilson loop operator.Comment: 6 pages, plain tex

Eternity and the cosmological constant

The purpose of this paper is to analyze the stability of interacting matter in the presence of a cosmological constant. Using an approach based on the heat equation, no imaginary part is found for the effective potential in the presence of a fixed background, which is the n-dimensional sphere or else an analytical continuation thereof, which is explored in some detail.Comment: 45 pages, 6 figure

QCD Strings as Constrained Grassmannian Sigma Model:

We present calculations for the effective action of string world sheet in R3 and R4 utilizing its correspondence with the constrained Grassmannian sigma model. Minimal surfaces describe the dynamics of open strings while harmonic surfaces describe that of closed strings. The one-loop effective action for these are calculated with instanton and anti-instanton background, reprsenting N-string interactions at the tree level. The effective action is found to be the partition function of a classical modified Coulomb gas in the confining phase, with a dynamically generated mass gap.Comment: 22 pages, Preprint: SFU HEP-116-9

A Mechanism for Ferrimagnetism and Incommensurability in One-Dimensional Systems

A mechanism for ferrimagnetism in (1+1)-dimensions is discussed. The ferrimagnetism is cased by interactions described by operators with non-zero conformal spin. Such interactions appear in such problems as the problem of tunneling between Luttinger liquids and the problem of frustrated spin ladder. I present exact solutions for a representative class of models containing such interactions together with a simple mean field analysis. It is shown that the interactions (i) dynamically generate static oscillations with a wave vector dependent on the coupling constant, (ii) give rise to a finite magnetic moment at $T = 0$ accompanied by the soft mode with a non-relativistic ({\it ferromagnetic}) dispersion $E \sim k^2$, (iii) generate massive (roton) modes.Comment: replaced by the extended version, references adde

Spectral properties of the one-dimensional two-channel Kondo lattice model

We have studied the energy spectrum of a one-dimensional Kondo lattice, where the localized magnetic moments have SU(N) symmetry and two channels of conduction electrons are present. At half filling, the system is shown to exist in two phases: one dominated by RKKY-exchange interaction effects, and the other by Kondo screening. A quantum phase transition point separates these two regimes at temperature $T = 0$. The Kondo-dominated phase is shown to possess soft modes, with spectral gaps much smaller than the Kondo temperature.Comment: 4 pages + 2 figures. Submitted for publicatio