192 research outputs found
On Exact Supersymmetry in DLCQ
In recent years a supersymmetric form of discrete light-cone quantization
(hereafter `SDLCQ') has emerged as a very powerful tool for solving
supersymmetric field theories. In this scheme, one calculates the light-cone
supercharge with respect to a discretized light-cone Fock basis, instead of
working with the light-cone Hamiltonian. This procedure has the advantage of
preserving supersymmetry even in the discretized theory, and eliminates the
need for explicit renormalizations in 1+1 dimensions. In order to compare the
usual DLCQ prescription with the supersymmetric prescription, we consider two
dimensional SU(N) Yang-Mills theory coupled to a massive adjoint Majorana
fermion, which is known to be supersymmetric at a particular value of the
fermion mass. After studying how singular-valued amplitudes and intermediate
zero momentum modes are regularized in both schemes, we are able to establish a
precise connection between conventional DLCQ and its supersymmetric extension,
SDLCQ. In particular, we derive the explicit form of the (irrelevant)
interaction that renders the DLCQ formulation of the theory exactly
supersymmetric for any light-cone compactification. We check our analytical
results via a numerical procedure, and discuss the relevance of this
interaction when supersymmetry is explicitly broken.Comment: 12 page
The Perils of `Soft' SUSY Breaking
We consider a two dimensional SU(N) gauge theory coupled to an adjoint
Majorana fermion, which is known to be supersymmetric for a particular value of
fermion mass. We investigate the `soft' supersymmetry breaking of the discrete
light cone quantization (DLCQ) of this theory. There are several DLCQ
formulations of this theory currently in the literature and they naively appear
to behave differently under `soft' supersymmetry breaking at finite resolution.
We show that all these formulations nevertheless yield identical bound state
masses in the decompactification limit of the light-like circle. Moreover, we
are able to show that the supersymmetry-inspired version of DLCQ (so called
`SDLCQ') provides the best rate of convergence of DLCQ bound state masses
towards the actual continuum values, except possibly near or at the critical
fermion mass. In this last case, we discuss improved extrapolation schemes that
must supplement the DLCQ algorithm in order to obtain correct continuum bound
state masses. Interestingly, when we truncate the Fock space to two particles,
the SDLCQ prescription presented here provides a scheme for improving the rate
of convergence of the massive t'Hooft model. Thus the supersymmetry-inspired
SDLCQ prescription is applicable to theories without supersymmetry.Comment: 11 pages, Latex; 2 figures (EPS); Numerical results extended;
conclusions revise
Exact Solution of the One-Dimensional Non-Abelian Coulomb Gas at Large N
The problem of computing the thermodynamic properties of a one-dimensional
gas of particles which transform in the adjoint representation of the gauge
group and interact through non-Abelian electric fields is formulated and solved
in the large limit. The explicit solution exhibits a first order
confinement-deconfinement phase transition with computable properties and
describes two dimensional adjoint QCD in the limit where matter field masses
are large.Comment: 8 pages, late
Adsorption models of hybridization and post-hybridisation behaviour on oligonucleotide microarrays
Analysis of data from an Affymetrix Latin Square spike-in experiment
indicates that measured fluorescence intensities of features on an
oligonucleotide microarray are related to spike-in RNA target concentrations
via a hyperbolic response function, generally identified as a Langmuir
adsorption isotherm. Furthermore the asymptotic signal at high spike-in
concentrations is almost invariably lower for a mismatch feature than for its
partner perfect match feature. We survey a number of theoretical adsorption
models of hybridization at the microarray surface and find that in general they
are unable to explain the differing saturation responses of perfect and
mismatch features. On the other hand, we find that a simple and consistent
explanation can be found in a model in which equilibrium hybridization followed
by partial dissociation of duplexes during the post-hybridization washing
phase.Comment: 26 pages, 6 figures, some rearrangement of sections and some
additions. To appear in J.Phys.(condensed matter
Scaling Study of Pure Gauge Lattice QCD by Monte Carlo Renormalization Group Method
The scaling behavior of pure gauge SU(3) in the region is
examined by a Monte Carlo Renormalization Group analysis. The coupling shifts
induced by factor 2 blocking are measured both on 32 and 16 lattices
with high statistics. A systematic deviation from naive 2-loop scaling is
clearly seen. The mean field and effective coupling constant schemes explain
part, but not all of the deviation. It can be accounted for by a suitable
change of coupling constant, including a correction term in the
2-loop lattice -function. Based on this improvement,
is estimated to be from the analysis of the string tension .Comment: 4 pages of A4 format including 7-postscript figure
On the Spectrum of QCD(1+1) with SU(N_c) Currents
Extending previous work, we calculate in this note the fermionic spectrum of
two-dimensional QCD (QCD_2) in the formulation with SU(N_c) currents. Together
with the results in the bosonic sector this allows to address the as yet
unresolved task of finding the single-particle states of this theory as a
function of the ratio of the numbers of flavors and colors, \lambda=N_f/N_c,
anew. We construct the Hamiltonian matrix in DLCQ formulation as an algebraic
function of the harmonic resolution K and the continuous parameter \lambda.
Amongst the more surprising findings in the fermionic sector chiefly considered
here is that the fermion momentum is a function of \lambda. This dependence is
necessary in order to reproduce the well-known 't Hooft and large N_f spectra.
Remarkably, those spectra have the same single-particle content as the ones in
the bosonic sectors. The twist here is the dramatically different sizes of the
Fock bases in the two sectors, which makes it possible to interpret in
principle all states of the discrete approach. The hope is that some of this
insight carries over into the continuum. We also present some new findings
concerning the single-particle spectrum of the adjoint theory.Comment: 21 pp., 13 figures, version published in PR
Surface induced disorder in body-centered cubic alloys
We present Monte Carlo simulations of surface induced disordering in a model
of a binary alloy on a bcc lattice which undergoes a first order bulk
transition from the ordered DO3 phase to the disordered A2 phase. The data are
analyzed in terms of an effective interface Hamiltonian for a system with
several order parameters in the framework of the linear renormalization
approach due to Brezin, Halperin and Leibler. We show that the model provides a
good description of the system in the vicinity of the interface. In particular,
we recover the logarithmic divergence of the thickness of the disordered layer
as the bulk transition is approached, we calculate the critical behavior of the
maxima of the layer susceptibilities, and demonstrate that it is in reasonable
agreement with the simulation data. Directly at the (110) surface, the theory
predicts that all order parameters vanish continuously at the surface with a
nonuniversal, but common critical exponent. However, we find different
exponents for the order parameter of the DO3 phase and the order parameter of
the B2 phase. Using the effective interface model, we derive the finite size
scaling function for the surface order parameter and show that the theory
accounts well for the finite size behavior of the DO3 ordering but not for that
of B2 ordering. The situation is even more complicated in the neighborhood of
the (100) surface, due to the presence of an ordering field which couples to
the B2 order.Comment: To appear in Physical Review
Physics of Quark--Gluon Plasma
In this lecture, we give a brief review of what theorists now know,
understand, or guess about static and kinetic properties of quark--gluon
plasma. A particular attention is payed to the problem of physical
observability, i.e. the physical meaningfulness of various characteristics of
discussed in the literature.Comment: 35 pages LaTeX, 3 Postscript figures included by epsf.sty are now
fixed and printable, uses axodraw.sty included in the package. Some
references added and minor stylistic changes made. Lecture at the XXIV ITEP
Winter School (Snegiri, February 1996
Asymptotic Energy Dependence of Hadronic Total Cross Sections from Lattice QCD
The nonperturbative approach to soft high-energy hadron-hadron scattering,
based on the analytic continuation of Wilson-loop correlation functions from
Euclidean to Minkowskian theory, allows to investigate the asymptotic energy
dependence of hadron-hadron total cross sections in lattice QCD. In this paper
we will show, using best fits of the lattice data with proper functional forms
satisfying unitarity and other physical constraints, how indications emerge in
favor of a universal asymptotic high-energy behavior of the kind B log^2 s for
hadronic total cross sections.Comment: Revised and extended version; 29 pages, 4 figure
Colour-Dielectric Gauge Theory on a Transverse Lattice
We investigate in some detail consequences of the effective colour-dielectric
formulation of lattice gauge theory using the light-cone Hamiltonian formalism
with a transverse lattice. As a quantitative test of this approach, we have
performed extensive analytic and numerical calculations for 2+1-dimensional
pure gauge theory in the large N limit. Because of Eguchi-Kawai reduction, one
effectively studies a 1+1-dimensional gauge theory coupled to matter in the
adjoint representation. We study the structure of coupling constant space for
our effective potential by comparing with the physical results available from
conventional Euclidean lattice Monte Carlo simulations of this system. In
particular, we calculate and measure the scaling behaviour of the entire
low-lying glueball spectrum, glueball wavefunctions, string tension, asymptotic
density of states, and deconfining temperature. We employ a new hybrid
DLCQ/wavefunction basis in our calculations of the light-cone Hamiltonian
matrix elements, along with extrapolation in Tamm-Dancoff truncation,
significantly reducing numerical errors. Finally we discuss, in light of our
results, what further measurements and calculations could be made in order to
systematically remove lattice spacing dependence from our effective potential a
priori.Comment: 48 pages, Latex, uses macro boxedeps.tex, minor errors corrected in
revised versio
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