165 research outputs found
Once more on the Witten index of 3d supersymmetric YM-CS theory
The problem of counting the vacuum states in the supersymmetric 3d
Yang-Mills-Chern-Simons theory is reconsidered. We resolve the controversy
between its original calculation by Witten at large volumes and the calculation
based on the evaluation of the effective Lagrangian in the small volume limit.
We show that the latter calculation suffers from uncertainties associated with
the singularities in the moduli space of classical vacua where the
Born-Oppenheimer approximation breaks down. We also show that these
singularities can be accurately treated in the Hamiltonian Born-Oppenheimer
method, where one has to match carefully the effective wave functions on the
Abelian valley and the wave functions of reduced non-Abelian QM theory near the
singularities. This gives the same result as original Witten's calculation.Comment: 27 page
The critical behaviour of Ising spins on 2D Regge lattices
We performed a high statistics simulation of Ising spins coupled to 2D
quantum gravity on toroidal geometries. The tori were triangulated using the
Regge calculus approach and contained up to vertices. We used a
constant area ensemble with an added interaction term, employing the
measure. We find clear evidence that the critical exponents of the Ising
phase transition are consistent with the static critical exponents and do not
depend on the coupling strength of the interaction term. We definitively
can exclude for this type of model a behaviour as predicted by Boulatov and
Kazakov [Phys. Lett. {\bf B186}, 379 (1987)] for Ising spins coupled to
dynamically triangulated surfaces.Comment: 15 pages with 3 figures in form of an uudecoded compressed
tar-ps-file. FUB-HEP 06/9
Dynamically Triangulated Ising Spins in Flat Space
A model describing Ising spins with short range interactions moving randomly
in a plane is considered. In the presence of a hard core repulsion, which
prevents the Ising spins from overlapping, the model is analogous to a
dynamically triangulated Ising model with spins constrained to move on a flat
surface. It is found that as a function of coupling strength and hard core
repulsion the model exhibits multicritical behavior, with first and second
order transition lines terminating at a tricritical point. The thermal and
magnetic exponents computed at the tricritical point are consistent with the
exact two-matrix model solution of the random Ising model, introduced
previously to describe the effects of fluctuating geometries.Comment: (10 pages + 4 figures), CERN-Th-7577/9
String Effects in the Wilson Loop: a high precision numerical test
We test numerically the effective string description of the infrared limit of
lattice gauge theories in the confining regime. We consider the 3d Z(2) lattice
gauge theory, and we define ratios of Wilson loops such that the predictions of
the effective string theory do not contain any adjustable parameters. In this
way we are able to obtain a degree of accuracy high enough to show
unambiguously that the flux--tube fluctuations are described, in the infrared
limit, by an effective bosonic string theory.Comment: 19 pages, LaTeX file + two .eps figure
Screening and Deconfinement of Sources in Finite Temperature SU(2) Lattice Gauge Theory
Deconfinement and screening of higher-representation sources in
finite-temperature lattice gauge theory is investigated by both
analytical and numerical means. The effective Polyakov-line action at strong
coupling is simulated by an efficient cluster-updating Monte Carlo algorithm
for the case of dimensions. The results compare very favourably with
an improved mean-field solution. The limit of the
theory is shown to be highly singular as far as critical behaviour is
concerned. In that limit the leading amplitudes of higher representation
Polyakov lines vanish at strong coupling, and subleading exponents become
dominant. Each of the higher-representation sources then effectively carry with
them their own critical exponents.Comment: 13pages+7figures, CERN-TH-7222/94 One reference added, else unchange
Multiple Potts Models Coupled to Two-Dimensional Quantum Gravity
We perform Monte Carlo simulations using the Wolff cluster algorithm of {\it
multiple} state Potts models on dynamical phi-cubed graphs of
spherical topology in order to investigate the region of two-dimensional
quantum gravity. Contrary to naive expectation we find no obvious signs of
pathological behaviour for . We discuss the results in the light of
suggestions that have been made for a modified DDK ansatz for .Comment: 9 page
Noncomputability Arising In Dynamical Triangulation Model Of Four-Dimensional Quantum Gravity
Computations in Dynamical Triangulation Models of Four-Dimensional Quantum
Gravity involve weighted averaging over sets of all distinct triangulations of
compact four-dimensional manifolds. In order to be able to perform such
computations one needs an algorithm which for any given and a given compact
four-dimensional manifold constructs all possible triangulations of
with simplices. Our first result is that such algorithm does not
exist. Then we discuss recursion-theoretic limitations of any algorithm
designed to perform approximate calculations of sums over all possible
triangulations of a compact four-dimensional manifold.Comment: 8 Pages, LaTex, PUPT-132
Measuring the string susceptibility in 2D simplicial quantum gravity using the Regge approach
We use Monte Carlo simulations to study pure 2D Euclidean quantum gravity
with -interaction on spherical topologies, employing Regge's formulation.
We attempt to measure the string susceptibility exponent by
using a finite-size scaling Ansatz in the expectation value of , as has
been done in a previous study by Bock and Vink ( hep-lat/9406018 ). By
considerably extending the range and statistics of their study we find that
this Ansatz is plagued by large systematic errors. The specific string
susceptibility exponent \GS' is found to agree with theoretical predictions,
but its determination also is subject to large systematic errors and the
presence of finite-size scaling corrections. To circumvent this obstacle we
suggest a new scaling Ansatz which in principle should be able to predict both,
\GS and \GS'. First results indicate that this requires large system sizes
to reduce the uncertainties in the finite-size scaling Ans\"atze. Nevertheless,
our investigation shows that within the achievable accuracy the numerical
estimates are still compatible with analytic predictions, contrary to the
recent claim by Bock and Vink.Comment: 33 pages, self unpacking uuencoded PostScript file, including all the
figures. Paper also available at http://www.physik.fu-berlin.de/~holm
D-Theory: Field Theory via Dimensional Reduction of Discrete Variables
A new non-perturbative approach to quantum field theory --- D-theory --- is
proposed, in which continuous classical fields are replaced by discrete
quantized variables which undergo dimensional reduction. The 2-d classical O(3)
model emerges from the (2+1)-d quantum Heisenberg model formulated in terms of
quantum spins. Dimensional reduction is demonstrated explicitly by simulating
correlation lengths up to 350,000 lattice spacings using a loop cluster
algorithm. In the framework of D-theory, gauge theories are formulated in terms
of quantum links --- the gauge analogs of quantum spins. Quantum links are
parallel transporter matrices whose elements are non-commuting operators. They
can be expressed as bilinears of anticommuting fermion constituents. In quantum
link models dimensional reduction to four dimensions occurs, due to the
presence of a 5-d Coulomb phase, whose existence is confirmed by detailed
simulations using standard lattice gauge theory. Using Shamir's variant of
Kaplan's fermion proposal, in quantum link QCD quarks appear as edge states of
a 5-d slab. This naturally protects their chiral symmetries without
fine-tuning. The first efficient cluster algorithm for a gauge theory with a
continuous gauge group is formulated for the U(1) quantum link model. Improved
estimators for Wilson loops are constructed, and dimensional reduction to
ordinary lattice QED is verified numerically.Comment: 15 pages, LaTeX, including 9 encapsulated postscript figures.
Contribution to Lattice 97 by 5 authors, to appear in Nuclear Physics B
(Proceeding Supplements). Requires psfig.tex and espcrc2.st
The deconfinement transition of finite density QCD with heavy quarks from strong coupling series
Starting from Wilson's action, we calculate strong coupling series for the
Polyakov loop susceptibility in lattice gauge theories for various small N_\tau
in the thermodynamic limit. Analysing the series with Pad\'e approximants, we
estimate critical couplings and exponents for the deconfinement phase
transition. For SU(2) pure gauge theory our results agree with those from
Monte-Carlo simulations within errors, which for the coarser N_\tau=1,2
lattices are at the percent level. For QCD we include dynamical fermions via a
hopping parameter expansion. On a N_\tau=1 lattice with N_f=1,2,3, we locate
the second order critical point where the deconfinement transition turns into a
crossover. We furthermore determine the behaviour of the critical parameters
with finite chemical potential and find the first order region to shrink with
growing \mu. Our series moreover correctly reflects the known Z(N) transition
at imaginary chemical potential.Comment: 18 pages, 7 figures, typos corrected, version published in JHE
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