2,059 research outputs found
Gluon Chain Model of the Confining Force
We develop a picture of the QCD string as a chain of constituent gluons,
bound by attractive nearest-neighbor forces which may be treated
perturbatively. This picture accounts for both Casimir scaling at large N, and
the asymptotic center dependence of the static quark potential. We discuss the
relevance, to the gluon-chain picture, of recent three-loop results for the
static quark potential. A variational framework is presented for computing the
minimal energy and wavefunction of a long gluon chain, which enables us to
derive both the logarithmic broadening of the QCD flux tube (``roughening''),
and the existence of a Luscher -c/R term in the potential.Comment: 25 pages, 5 figures, latex2
Scattering of Glue by Glue on the Light-cone Worldsheet I: Helicity Non-conserving Amplitudes
We give the light-cone gauge calculation of the one-loop on-shell scattering
amplitudes for gluon-gluon scattering which violate helicity conservation. We
regulate infrared divergences by discretizing the p^+ integrations, omitting
the terms with p^+=0. Collinear divergences are absent diagram by diagram for
the helicity non-conserving amplitudes. We also employ a novel ultraviolet
regulator that is natural for the light-cone worldsheet description of planar
Feynman diagrams. We show that these regulators give the known answers for the
helicity non-conserving one-loop amplitudes, which don't suffer from the usual
infrared vagaries of massless particle scattering. For the maximal helicity
violating process we elucidate the physics of the remarkable fact that the loop
momentum integrand for the on-shell Green function associated with this
process, with a suitable momentum routing of the different contributing
topologies, is identically zero. We enumerate the counterterms that must be
included to give Lorentz covariant results to this order, and we show that they
can be described locally in the light-cone worldsheet formulation of the sum of
planar diagrams.Comment: 30 pages, 17 figure
Calculating the Rest Tension for a Polymer of String Bits
We explore the application of approximation schemes from many body physics,
including the Hartree-Fock method and random phase approximation (RPA), to the
problem of analyzing the low energy excitations of a polymer chain made up of
bosonic string bits. We accordingly obtain an expression for the rest tension
of the bosonic relativistic string in terms of the parameters
characterizing the microscopic string bit dynamics. We first derive an exact
connection between the string tension and a certain correlation function of the
many-body string bit system. This connection is made for an arbitrary
interaction potential between string bits and relies on an exact dipole sum
rule. We then review an earlier calculation by Goldstone of the low energy
excitations of a polymer chain using RPA. We assess the accuracy of the RPA by
calculating the first order corrections. For this purpose we specialize to the
unique scale invariant potential, namely an attractive delta function potential
in two (transverse) dimensions. We find that the corrections are large, and
discuss a method for summing the large terms. The corrections to this improved
RPA are roughly 15\%.Comment: 44 pages, phyzzx, psfig required, Univ. of Florida preprint,
UFIFT-HEP-94
Spontaneous Symmetry Breaking at Infinite Momentum without P+ Zero-Modes
The nonrelativistic interpretation of quantum field theory achieved by
quantization in an infinite momentum frame is spoiled by the inclusion of a
mode of the field carrying p+=0. We therefore explore the viability of doing
without such a mode in the context of spontaneous symmetry breaking (SSB),
where its presence would seem to be most needed. We show that the physics of
SSB in scalar quantum field theory in 1+1 space-time dimensions is accurately
described without a zero-mode.Comment: LaTeX, 8 pages, 3 eps figure
String Bit Models for Superstring
We extend the model of string as a polymer of string bits to the case of
superstring. We mainly concentrate on type II-B superstring, with some
discussion of the obstacles presented by not II-B superstring, together with
possible strategies for surmounting them. As with previous work on bosonic
string we work within the light-cone gauge. The bit model possesses a good deal
less symmetry than the continuous string theory. For one thing, the bit model
is formulated as a Galilei invariant theory in dimensional
space-time. This means that Poincar\'e invariance is reduced to the Galilei
subgroup in space dimensions. Naturally the supersymmetry present in the
bit model is likewise dramatically reduced. Continuous string can arise in the
bit models with the formation of infinitely long polymers of string bits. Under
the right circumstances (at the critical dimension) these polymers can behave
as string moving in dimensional space-time enjoying the full
Poincar\'e supersymmetric dynamics of type II-B superstring.Comment: 43 pages, phyzzx require
Scattering of Glue by Glue on the Light-cone Worldsheet II: Helicity Conserving Amplitudes
This is the second of a pair of articles on scattering of glue by glue, in
which we give the light-cone gauge calculation of the one-loop on-shell
helicity conserving scattering amplitudes for gluon-gluon scattering
(neglecting quark loops). The 1/p^+ factors in the gluon propagator are
regulated by replacing p^+ integrals with discretized sums omitting the p^+=0
terms in each sum. We also employ a novel ultraviolet regulator that is
convenient for the light-cone worldsheet description of planar Feynman
diagrams. The helicity conserving scattering amplitudes are divergent in the
infra-red. The infrared divergences in the elastic one-loop amplitude are shown
to cancel, in their contribution to cross sections, against ones in the cross
section for unseen bremsstrahlung gluons. We include here the explicit
calculation of the latter, because it assumes an unfamiliar form due to the
peculiar way discretization of p^+ regulates infrared divergences. In resolving
the infrared divergences we employ a covariant definition of jets, which allows
a transparent demonstration of the Lorentz invariance of our final results.
Because we use an explicit cutoff of the ultraviolet divergences in exactly 4
space-time dimensions, we must introduce explicit counterterms to achieve this
final covariant result. These counter-terms are polynomials in the external
momenta of the precise order dictated by power-counting. We discuss the
modifications they entail for the light-cone worldsheet action that reproduces
the ``bare'' planar diagrams of the gluonic sector of QCD. The simplest way to
do this is to interpret the QCD string as moving in six space-time dimensions.Comment: 56 pages, 21 figures, references added, minor typos correcte
Bag Model for a Link in a Closed Gluonic Chain
The large limit of Yang-Mills gauge theory is the dynamics of a closed
gluonic chain, but this fact does not obviate the inherently strong coupling
nature of the dynamical problem. However, we suggest that a single link in such
a chain might be reasonably described in the quasi-perturbative language of
gluons and their interactions. To implement this idea, we use the MIT bag to
model the physics of a nearest neighbor bond.Comment: 10 pages, LaTe
More On The Connection Between Planar Field Theory And String Theory
We continue work on the connection between world sheet representation of the
planar phi^3 theory and string formation. The present article, like the earlier
work, is based on the existence of a solitonic solution on the world sheet, and
on the zero mode fluctuations around this solution. The main advance made in
this paper is the removal of the cutoff and the transition to the continuum
limit on the world sheet. The result is an action for the modes whose energies
remain finite in this limit (light modes). The expansion of this action about a
dense background of graphs on the world sheet leads to the formation of a
string.Comment: 27 pages, 3 figure
Field Theory On The World Sheet: Improvements And Generalizations
This article is the continuation of a project of investigating planar phi^3
model in various dimensions. The idea is to reformulate them on the world
sheet, and then to apply the classical (meanfield) approximation, with two
goals: To show that the ground state of the model is a solitonic configuration
on the world sheet, and the quantum fluctuations around the soliton lead to the
formation of a transverse string. After a review of some of the earlier work,
we introduce and discuss several generalizations and new results. In 1+2
dimensions, a rigorous upper bound on the solitonic energy is established. A
phi^4 interaction is added to stabilize the original phi^3 model. In 1+3 and
1+5 dimensions, an improved treatment of the ultraviolet divergences is given.
And significantly, we show that our approximation scheme can be imbedded into a
systematic strong coupling expansion. Finally, the spectrum of quantum
fluctuations around the soliton confirms earlier results: In 1+2 and 1+3
dimensions, a transverse string is formed on the world sheet.Comment: 29 pages, 5 figures, several typos and eqs.(74) and (75) are
corrected, a comment added to section
Quantum Newtonian Dynamics on a Light Front
We recall the special features of quantum dynamics on a light-front (in an
infinite momentum frame) in string and field theory. The reason this approach
is more effective for string than for fields is stressed: the light-front
dynamics for string is that of a true Newtonian many particle system, since a
string bit has a fixed Newtonian mass. In contrast, each particle of a field
theory has a variable Newtonian mass P^+, so the Newtonian analogy actually
requires an infinite number of species of elementary Newtonian particles. This
complication substantially weakens the value of the Newtonian analogy in
applying light-front dynamics to nonperturbative problems. Motivated by the
fact that conventional field theories can be obtained as infinite tension
limits of string theories, we propose a way to recast field theory as a
standard Newtonian system. We devise and analyze some simple quantum mechanical
systems that display the essence of the proposal, and we discuss prospects for
applying these ideas to large N_c QCD.Comment: 13 pages, 3 figures, LaTex, psfig, references added, APS copyrigh
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