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Peter Orland

Publications and source records attributed to Peter Orland.

34 records · Page 2Linked to original sources
arXiv2007

Glueball Masses in (2+1)-Dimensional Anisotropic Weakly-Coupled Yang-Mills Theory

The confinement problem has been solved in the anisotropic (2+1)-dimensional SU(N) Yang-Mills theory at weak coupling. In this paper, we find the low-lying spectrum for N=2. The lightest excitations are pairs of fundamental particles of the (1+1)-dimensional SU(2)XSU(2) principal chiral sigma model bound in a linear potential, with a specified matching condition where the particles overlap. This matching condition can be determined from the exactly-known S-matrix for the sigma model.

hep-th↗
arXiv2006

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.

hep-th↗
arXiv2006

Integrable Models and Confinement in (2+1)-Dimensional Weakly-Coupled Yang-Mills Theory

We generalize the (2+1)-dimensional Yang-Mills theory to an anisotropic form with two gauge coupling constants $e$ and $e^{\prime}$. In an axial gauge, a regularized version of the Hamiltonian of this gauge theory is $H_{0}+{e^{\prime}}^{2}H_{1}$, where $H_{0}$ is the Hamiltonian of a set of (1+1)-dimensional principal chiral nonlinear sigma models. We treat $H_{1}$ as the interaction Hamiltonian. For gauge group SU(2), we use form factors of the currents of the principal chiral sigma models to compute the string tension for small $e^{\prime}$, after reviewing exact S-matrix and form-factor methods. In the anisotropic regime, the dependence of the string tension on the coupling constant is not in accord with generally-accepted dimensional arguments.

hep-th↗
arXiv2005

Asymptotic Freedom of Elastic Strings and Barriers

We study the problem of a quantized elastic string in the presence of an impenetrable wall. This is a two-dimensional field theory of an N-component real scalar field $ϕ$ which becomes interacting through the restriction that the magnitude of $ϕ$ is less than $ϕ_{\rm max}$, for a spherical wall of radius $ϕ_{\rm max}$. The N=1 case is a string vibrating in a plane between two straight walls. We review a simple nonperturbative argument that there is a gap in the spectrum, with asymptotically-free behavior in the coupling (which is the reciprocal of $ϕ_{\rm max}$) for N greater than or equal to one. This scaling behavior of the mass gap has been disputed in some of the recent literature. We find, however, that perturbation theory and the 1/N expansion each confirms that these theories are asymptotically free. The large N limit coincides with that of the O(N) nonlinear sigma model. A theta parameter exists for the N=2 model, which describes a string confined to the interior of a cylinder of radius $ϕ_{\rm max}$.

cond-mat.stat-mech↗
arXiv2005

Lattice QCD-2+1

We consider a 2+1-dimensional SU(N) lattice gauge theory in an axial gauge with the link field U in the 1-direction set to one. The term in the Hamiltonian containing the square of the electric field in the 1-direction is non-local. Despite this non-locality, we show that weak-coupling perturbation theory in this term gives a finite vacuum-energy density to second order, and suggest that this property holds to all orders. Heavy quarks are confined, the spectrum is gapped, and the space-like Wilson loop has area decay.

hep-lat↗
arXiv2004

Gauge-Invariant Coordinates on Gauge-Theory Orbit Space

A gauge-invariant field is found which describes physical configurations, i.e. gauge orbits, of non-Abelian gauge theories. This is accomplished with non-Abelian generalizations of the Poincare'-Hodge formula for one-forms. In a particular sense, the new field is dual to the gauge field. Using this field as a coordinate, the metric and intrinsic curvature are discussed for Yang-Mills orbit space for the (2+1)- and (3+1)-dimensional cases. The sectional, Ricci and scalar curvatures are all formally non-negative. An expression for the new field in terms of the Yang-Mills connection is found in 2+1 dimensions. The measure on Schroedinger wave functionals is found in both 2+1 and 3+1 dimensions; in the former case, it resembles Karabali, Kim and Nair's measure. We briefly discuss the form of the Hamiltonian in terms of the dual field and comment on how this is relevant to the mass gap for both the (2+1)- and (3+1)-dimensional cases.

hep-th↗
arXiv2001

Evolution of Fixed-End Strings and the Off-Shell Disk Amplitude

An exact integral expression is found for the amplitude of a Bosonic string with ends separated by a fixed distance $R$ evolving over a time $T$ between arbitrary initial and final configurations. It is impossible to make a covariant subtraction of a covariant quantity which would render the amplitude non-zero. It is suggested that this fact (and not the tachyon) is responsible for the lack of a continuum limit of regularized random-surface models with target-space dimension greater than one. It appears consistent, however, to remove this quantity by hand. The static potential of Alvarez and Arvis $V(R)$ is recovered from the resulting finite amplitude for $R>R_{c}$. For $R<R_{c}$, we find $V(R)=-\infty$, instead of the usual tachyonic result. A rotation-invariant expression is proposed for special cases of the off-shell disk amplitude. {\it None} of the finite amplitudes discussed are Nambu or Polyakov functional integrals, except through an unphysical analytic continuation. We argue that the Liouville field does not decouple in off-shell amplitudes, even when the space-time dimension is twenty-six.

hep-th↗
arXiv2000

Extremal Curves in 2+1-Dimensional Yang-Mills Theory

We examine the structure of the potential energy of 2+1-dimensional Yang-Mills theory on a torus with gauge group SU(2). We use a standard definition of distance on the space of gauge orbits. A curve of extremal potential energy in orbit space defines connections satisfying a certain partial differential equation. We argue that the energy spectrum is gapped because the extremal curves are of finite length. Though classical gluon waves satisfy our differential equation, they are not extremal curves. We construct examples of extremal curves and find how the length of these curves depends on the dimensions of the torus. The intersections with the Gribov horizon are determined explicitly. The results are discussed in the context of Feynman's ideas about the origin of the mass gap.

hep-th↗
arXiv1997

Potential Topography and Mass Generation

We describe an approach to understanding exponential decay of correlation functions in asymptotically free theories. This approach is systematic; it does not start from any conjectured mechanism or picture. We begin by studying the metric on the space of configurations and the behavior of the potential-energy function on this space. We describe how these ideas fit in the framework of QCD, as discussed earlier by one of us (P.O.). We then consider the 1+1-dimensional O(2) and O(3) nonlinear sigma models and show that no gap exists in the former at weak coupling. In the O(3) model a new kind of strong/weak-coupling duality is realized. We briefly outline our proposals for understanding the spectrum.

hep-th↗
arXiv1997

The Metric on the Space of Yang-Mills Configurations

A distance function on the set of physical equivalence classes of Yang-Mills configurations considered by Feynman and by Atiyah, Hitchin and Singer is studied for both the $2+1$ and $3+1$-dimensional Hamiltonians. This set equipped with this distance function is a metric space, and in fact a Riemannian manifold as Singer observed. Furthermore, this manifold is complete. Gauge configurations can be used to parametrize the manifold. The metric tensor without gauge fixing has zero eigenvalues, but is free of ambiguities on the entire manifold. In $2+1$ dimensions the problem of finding the distance from any configuration to a pure gauge configuration is an integrable system of two-dimensional differential equations. A calculus of manifolds with singular metric tensors is developed and the Riemann curvature is calculated using this calculus. The Laplacian on Yang-Mills wave functionals has a slightly different form from that claimed earlier. In $3+1$-dimensions there are field configurations an arbitrarily large distance from a pure gauge configuration with arbitrarily small potential energy. These configurations resemble long-wavelength gluons. Reasons why there nevertheless can be a mass gap in the quantum theory are proposed.

hep-th↗
arXiv1996

Lattice Bosonization

A free lattice fermion field theory in 1+1 dimensions can be interpreted as SOS-type model, whose spins are integer-valued. We point out that the relation between these spins and the fermion field is similar to the abelian bosonization relation between bosons and fermions in the continuum. Though on the lattice the connected $2n$-point correlation functions of the integer-valued spins are not zero for any $n \ge 1$, the two-point correlation function of these spins is that of free bosons in the infrared. We also conjecture the form of the Wess-Zumino-Witten chiral field operator in a nonabelian lattice fermion model. These constructions are similar in spirit to the ``twistable string" idea of Krammer and Nielsen.

hep-th↗
arXiv1994

Extrinsic Curvature Dependence of Nielsen-Olesen Strings

It is shown how to treat the degrees of freedom of Nielsen-Olesen vortices in the $3+1$-dimensional $U(1)$ higgs model by a collective coordinate method. In the london limit, where the higgs mass becomes infinite, the gauge and goldstone degrees of freedom are integrated out, resulting in the vortex world-sheet action. Introducing an ultraviolet cut-off mimics the effect of finite higgs mass. This action is non-polynomial in derivatives and depends on the extrinsic curvature of the surface. Flat surfaces are stable if the coherence length is less than the penetration depth. It is argued that in the quantum abelian higgs model, vortex world-sheets are dominated by branched polymers.

hep-th↗
arXiv1993

The Rokhsar-Kivelson Model of Quantum Dimers as a Gas of Free Fermionic Strings

The $2+1$-dimensional quantum dimer model on a square lattice, proposed by Rokhsar and Kivelson as a theory of layered superconductivity, is shown to be equivalent to a many-body theory of free, transversely oscillating strings obeying Fermi statistics. A Jordan-Wigner construction for string field operators is presented. Topological defects are shown to be linearly confined in pairs by dynamical strings. Exact upper and lower bounds are placed on the ground-state energy and the string tension. It is argued that the system is in a spin-fluid phase and that there is no gap in the excitation spectrum.

cond-mat↗
arXiv1993

The Space-Time Manifold as a Critical Solid

It is argued that the problems of the cosmological constant, stability and renormalizability of quantum gravity can be solved if the space-time manifold arises through spontaneous symmetry breaking. A ``pre-manifold" model is presented in which many points are connected by random bonds. A set of $D$ real numbers assigned to each point are coupled between points connected by bonds. It is then found that the dominant configuration of bonds is a flat $D$-dimensional manifold, on which there is a massless matter field. Long-wavelength fluctuations can describe quantized massless gravity if $D=\;4$, $6$, $8...$.

hep-th↗