237 research outputs found

### Composite Strings in (2+1)-Dimensional Anisotropic Weakly-Coupled Yang-Mills Theory

The small-scale structure of a string connecting a pair of static sources is
explored for the weakly-coupled anisotropic SU(2) Yang-Mills theory in (2+1)
dimensions. A crucial ingredient in the formulation of the string Hamiltonian
is the phenomenon of color smearing of the string constituents. The
quark-anti-quark potential is determined. We close with some discussion of the
standard, fully Lorentz-invariant Yang-Mills theory.Comment: Some minor errors corrected, references slightly reorganized, version
to appear in Phys. Rev.

### Confinement in (2+1)-Dimensional Gauge Theories at Weak Coupling

In axial gauge, the (2+1)-dimensional SU($N$) Yang-Mills theory is equivalent
to a set of (1+1)-dimensional integrable models with a non-local coupling
between charge densities. This fact makes it possible to determine the static
potential between charges at weak coupling in an anisotropic version of the
theory, and understand features of the spectrum.Comment: Four pages, Based on a talk given at ``Quark Confinement and the
Hadron Spectrum 7", Ponta Delgada, Sao Miguel, Azores, Portugal, Sept. 2-7,
200

### The universal coefficient of the exact correlator of a large-$N$ matrix field theory

Exact expressions have been proposed for correlation functions of the
large-$N$ (planar) limit of the $(1+1)$-dimensional ${\rm SU}(N)\times {\rm
SU}(N)$ principal chiral sigma model. These were obtained with the form-factor
bootstrap. The short-distance form of the two-point function of the scaling
field $\Phi(x)$, was found to be $N^{-1}\langle {\rm Tr}\,\Phi(0)^{\dagger}
\Phi(x)\rangle=C_{2}\ln^{2}mx$, where $m$ is the mass gap, in agreement with
the perturbative renormalization group. Here we point out that the universal
coefficient $C_{2}$, is proportional to the mean first-passage time of a
L\'{e}vy flight in one dimension. This observation enables us to calculate
$C_{2}=1/16\pi$.Comment: Text lengthened from 3 to 6 pages, to include discussion of previous
results and directions for further work. Some references added. Accepted for
publication in Phys. Rev.

### Longitudinal Rescaling of Quantum Electrodynamics

We investigate quantum longitudinal rescaling of electrodynamics,
transforming coordinates as $x^{0,3}\to\lambda x^{0,3}$ and $x^{1,2}\to
x^{1,2}$, to one loop. We do this by an aspherical Wilsonian renormalization,
which was applied earlier to pure Yang-Mills theory. We find the anomalous
powers of $\lambda$ in the renormalized couplings. Our result is only valid for
$\lambda \lesssim 1$, because perturbation theory breaks down for $\lambda \ll
1$.Comment: Version to appear in Phys. Rev.

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