21 research outputs found
Quasi-local Update Algorithms for Numerical Simulations of d=3 SU(2) LGT in the Dual Formulation
In the dual formulation of d=3 SU(2) LGT, the link variables are group
representations and valid configurations are those satisfying a number of
triangle inequalities. In \cite{lat99} algorithms for local updates that
automatically respect these constraints were described. It was also pointed out
there that these local updates were not ergodic. In this presentation, we
describe two different quasi-local updating algorithms which, in conjunction
with the local updates, appear to be ergodic.Comment: LATTICE2000(Topics in Gauge Theories),5 pages,5 figures,LaTe
Analytic Variational Investigation of Euclidean SU(3) Gauge Theory
Analytic variational techniques for lattice gauge theories based on the
Rayleigh-Ritz(RR) method were previously developed for euclidean SU(2) gauge
theories in 3 and 4 dimensions. Their extensions to SU(3) gauge theory
including applications to correlation functions and mass gaps are presented
here.Comment: 4-pages in 2-column format, typsetted for LaTeX with document style
espcrc2.sty (available on request), IMSc/93-2
Current Status of the Numerical Simulations of d=3 SU(2) Lattice Gauge Theory in the Dual Formulation
We have continued our systematic investigations of the numerical simulations
of lattice gauge theories in the dual formulation. These include: i) a more
practical implementation of the quasi-local updating technique, ii) a thorough
investigation of the sign problem, iii) issues related to the ergodicity of the
various update algorithms, iv) a novel way of measuring conventional
observables like plaquette in the dual formalism and v) investigations of
thermalisation. While the dual formulation holds out a lot of promises in
principle, there are still some ways to go before it can be made into an
attractive alternative lattice formulation.Comment: LATTICE2000(Topics in Gauge Theories),5 pages,3
figures,LaTex(espcrc2.sty
Continuum limit of string formation in 3-d SU(2) LGT
We study the continuum limit of the string-like behaviour of flux tubes
formed between static quarks and anti-quarks in three dimensional SU(2) lattice
gauge theory. We compare our simulation data with the predictions of both
effective string models as well as perturbation theory. On the string side we
obtain clear evidence for convergence of data to predictions of Nambu-Goto
theory. We comment on the scales at which the static potential starts departing
from one loop perturbation theory and then again being well described by
effective string theories. We also estimate the leading corrections to the
one-loop perturbative potential as well as the Nambu-Goto effective string. In
the intermediate regions we find that a modified Lennard-Jones type potential
gives surprisingly good fits.Comment: 13 pages, 3 figures and 6 table
String-like behaviour of 4d SU(3) Yang-Mills flux tubes
We present here results on the fine structure of the static q\bar q potential
in d=4 SU(3) Yang-Mills theory. The potential is obtained from Polyakov loop
correlators having separations between 0.3 and 1.2 fermi. Measurements were
carried out on lattices of spatial extents of about 4 and 5.4 fermi. The
temporal extent was 5.4 fermi in both cases. The results are analyzed in terms
of the force between a q\bar q pair as well as in terms of a scaled second
derivative of the potential. The data is accurate enough to distinguish between
different effective string models and it seems to favour the expression for
ground state energy of a Nambu-Goto string.Comment: 9 pages in LaTeX with 2 figures and 2 tables in JHEP style. Replaced
to match with shortened published versio
The confining string beyond the free-string approximation in the gauge dual of percolation
We simulate five different systems belonging to the universality class of the
gauge dual of three-dimensional random percolation to study the underlying
effective string theory at finite temperature. All the data for the finite
temperature string tension, when expressed by means of adimensional variables,
are nicely described by a unique scaling function. We calculate the first few
terms of the string tension up to order and compare to different
theoretical predictions. We obtain unambiguous evidence that the coefficients
of and terms coincide with those of the Nambu-Goto string, as
expected, while the term strongly differs and is characteristic of the
universality class of this specific gauge theory.Comment: 13 pages, 3 figure
Finite Size Effects for the Ising Model Coupled to 2-D Random Surfaces
Finite size effects for the Ising Model coupled to two dimensional random
surfaces are studied by exploiting the exact results from the 2-matrix models.
The fixed area partition function is numerically calculated with arbitrary
precision by developing an efficient algorithm for recursively solving the
quintic equations so encountered. An analytic method for studying finite size
effects is developed based on the behaviour of the free energy near its
singular points. The generic form of finite size corrections so obtained are
seen to be quite different from the phenomenological parameterisations used in
the literature. The method of singularities is also applied to study the
magnetic susceptibility. A brief discussion is presented on the implications of
these results to the problem of a reliable determination of string
susceptibility from numerical simulations.Comment: 18 pages, 3 figure
Parity and Time Reversal in the Spin-Rotation Interaction
A recently reported discrepancy between experimental and theoretical values
of the muon's g-2 factor is interpreted as due to small violations of the
conservation of P and T in the spin-rotation coupling. The experiments place an
upper limit on these violations and on the weight change of spinning
gyroscopes.Comment: 3 page
On the spectrum of closed k=2 flux tubes in D=2+1 SU(N) gauge theories
We calculate the energy spectrum of a k=2 flux tube that is closed around a
spatial torus, as a function of its length l. We do so for SU(4) and SU(5)
gauge theories in 2 space dimensions. We find that to a very good approximation
the eigenstates belong to the irreducible representations of the SU(N) group
rather than just to its center, Z_N. We obtain convincing evidence that the
low-lying states are, for l not too small, very close to those of the
Nambu-Goto free string theory (in flat space-time). The correction terms appear
to be typically of O(1) in appropriate units, much as one would expect if the
bosonic string model were an effective string theory for the dynamics of these
flux tubes. This is in marked contrast to the case of fundamental flux tubes
where such corrections have been found to be unnaturally small. Moreover we
find that these corrections appear to be particularly small when the `phonons'
along the string have the same momentum, and large when their momentum is
opposite. This provides information about the detailed nature of the
interactions in the effective string theory. We have searched for, but not
found, extra states that would arise from the excitation of the massive modes
presumably associated with the non-trivial structure of the flux tube.Comment: 37 pages, 16 figures, minor changes to text and figure
Asymptotically Free Non-Abelian Gauge Theories With Fermions and Scalars As Alternatives to QCD
In this paper we construct non-Abelian gauge theories with fermions and
scalars that nevertheless possess asymptotic freedom.The scalars are taken to
be in a chiral multiplet transforming as under
and transforming as singlets under the colour SU(3) group. We consider two
distinct scenarios, one in which the additional scalars are light and another
in which they are heavier than half the Z-boson mass. It is shown that
asymptotic freedom is obtained without requiring that all additional couplings
keep fixed ratios with each other. It is also shown that both scenarios can not
be ruled out by what are considered standard tests of QCD like R- parameter,
g-2 for muons or deep inelastic phenomena. The light mass scenario is however
ruled out by high precision Z-width data (and only by that one data).The heavy
mass scenario is still viable and is shown to naturally pass the test of
flavour changing neutral currents. It also is not ruled out by precision
electroweak oblique parameters. Many distinctive experimental signatures of
these models are also discussed.Comment: 37 pages in LATEX with 10 fig