2,118 research outputs found
Universality and Clustering in 1+1 Dimensional Superstring-Bit Models
We construct a 1+1 dimensional superstring-bit model for D=3 Type IIB
superstring. This low dimension model escapes the problems encountered in
higher dimension models: (1) It possesses full Galilean supersymmetry; (2) For
noninteracting polymers of bits, the exactly soluble linear superpotential
describing bit interactions is in a large universality class of superpotentials
which includes ones bounded at spatial infinity; (3) The latter are used to
construct a superstring-bit model with the clustering properties needed to
define an -matrix for closed polymers of superstring-bits.Comment: 11 pages, Latex documen
Defining the Force between Separated Sources on a Light Front
The Newtonian character of gauge theories on a light front requires that the
longitudinal momentum P^+, which plays the role of Newtonian mass, be
conserved. This requirement conflicts with the standard definition of the force
between two sources in terms of the minimal energy of quantum gauge fields in
the presence of a quark and anti-quark pinned to points separated by a distance
R. We propose that, on a light front, the force be defined by minimizing the
energy of gauge fields in the presence of a quark and an anti-quark pinned to
lines (1-branes) oriented in the longitudinal direction singled out by the
light front and separated by a transverse distance R. Such sources will have a
limited 1+1 dimensional dynamics. We study this proposal for weak coupling
gauge theories by showing how it leads to the Coulomb force law. For QCD we
also show how asymptotic freedom emerges by evaluating the S-matrix through one
loop for the scattering of a particle in the N_c representation of color
SU(N_c) on a 1-brane by a particle in the \bar N_c representation of color on a
parallel 1-brane separated from the first by a distance R<<1/Lambda_{QCD}.
Potential applications to the problem of confinement on a light front are
discussed.Comment: LaTeX, 15 pages, 12 figures; minor typos corrected; numerical
correction in equation 3.
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
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
Supersymmetric Quantum Mechanics for String-Bits
We develop possible versions of supersymmetric single particle quantum
mechanics, with application to superstring-bit models in view. We focus
principally on space dimensions , the transverse dimensionalities of
superstring in space-time dimensions. These are the cases for which
``classical'' superstring makes sense, and also the values of for which
Hooke's force law is compatible with the simplest superparticle dynamics. The
basic question we address is: When is it possible to replace such harmonic
force laws with more general ones, including forces which vanish at large
distances? This is an important question because forces between string-bits
that do not fall off with distance will almost certainly destroy cluster
decomposition. We show that the answer is affirmative for , negative for
, and so far inconclusive for .Comment: 17 pages, Late
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
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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