746 research outputs found
Non-Douglas-Kazakov phase transition of two-dimensional generalized Yang-Mills theories
In two-dimensional Yang-Mills and generalized Yang-Mills theories for large
gauge groups, there is a dominant representation determining the thermodynamic
limit of the system. This representation is characterized by a density the
value of which should everywhere be between zero and one. This density itself
is determined through a saddle-point analysis. For some values of the parameter
space, this density exceeds one in some places. So one should modify it to
obtain an acceptable density. This leads to the well-known Douglas-Kazakov
phase transition. In generalized Yang-Mills theories, there are also regions in
the parameter space where somewhere this density becomes negative. Here too,
one should modify the density so that it remains nonnegative. This leads to
another phase transition, different from the Douglas-Kazakov one. Here the
general structure of this phase transition is studied, and it is shown that the
order of this transition is typically three. Using carefully-chosen parameters,
however, it is possible to construct models with phase-transition orders not
equal to three. A class of these non-typical models are also studied.Comment: 11 pages, accepted for publication in Eur. Phys. J.
On the modification of the Efimov spectrum in a finite cubic box
Three particles with large scattering length display a universal spectrum of
three-body bound states called "Efimov trimers''. We calculate the modification
of the Efimov trimers of three identical bosons in a finite cubic box and
compute the dependence of their energies on the box size using effective field
theory. Previous calculations for positive scattering length that were
perturbative in the finite volume energy shift are extended to arbitrarily
large shifts and negative scattering lengths. The renormalization of the
effective field theory in the finite volume is explicitly verified. Moreover,
we investigate the effects of partial wave mixing and study the behavior of
shallow trimers near the dimer energy. Finally, we provide numerical evidence
for universal scaling of the finite volume corrections.Comment: 21 pages, 8 figures, published versio
Branes as Stable Holomorphic Line Bundles On the Non-Commutative Torus
It was recently suggested by A. Kapustin that turning on a -field, and
allowing some discrepancy between the left and and right-moving complex
structures, must induce an identification of B-branes with holomorphic line
bundles on a non-commutative complex torus. We translate the stability
condition for the branes into this language and identify the stable topological
branes with previously proposed non-commutative instanton equations. This
involves certain topological identities whose derivation has become familiar in
non-commutative field theory. It is crucial for these identities that the
instantons are localized. We therefore explore the case of non-constant field
strength, whose non-linearities are dealt with thanks to the rank-one
Seiberg--Witten map.Comment: 12 pages, LaTe
Particle Production in Matrix Cosmology
We consider cosmological particle production in 1+1 dimensional string
theory. The process is described most efficiently in terms of anomalies, but we
also discuss the explicit mode expansions. In matrix cosmology the usual vacuum
ambiguity of quantum fields in time-dependent backgrounds is resolved by the
underlying matrix model. This leads to a finite energy density for the "in"
state which cancels the effect of anomalous particle production.Comment: 24 pages, 1 figure; v2: references added, minor change
Decoupling of Degenerate Positive-norm States in Witten's String Field Theory
We show that the degenerate positive-norm physical propagating fields of the
open bosonic string can be gauged to the higher rank fields at the same mass
level. As a result, their scattering amplitudes can be determined from those of
the higher spin fields. This phenomenon arises from the existence of two types
of zero-norm states with the same Young representations as those of the
degenerate positive-norm states in the old covariant first quantized (OCFQ)
spectrum. This is demonstrated by using the lowest order gauge transformation
of Witten's string field theory (WSFT) up to the fourth massive level
(spin-five), and is found to be consistent with conformal field theory
calculation based on the first quantized generalized sigma-model approach. In
particular, on-shell conditions of zero-norm states in OCFQ stringy gauge
transformation are found to correspond, in a one-to-one manner, to the
background ghost fields in off-shell gauge transformation of WSFT. The
implication of decoupling of scalar modes on Sen's conjectures was also briefly
discussed.Comment: 18 pages, use Latex with revtex
Quantum theory as a relevant framework for the statement of probabilistic and many-valued logic
Based on ideas of quantum theory of open systems we propose the consistent
approach to the formulation of logic of plausible propositions. To this end we
associate with every plausible proposition diagonal matrix of its likelihood
and examine it as density matrix of relevant quantum system. We are showing
that all logical connectives between plausible propositions can be represented
as special positive valued transformations of these matrices. We demonstrate
also the above transformations can be realized in relevant composite quantum
systems by quantum engineering methods. The approach proposed allows one not
only to reproduce and generalize results of well-known logical systems
(Boolean, Lukasiewicz and so on) but also to classify and analyze from unified
point of view various actual problems in psychophysics and social sciences.Comment: 7 page
Strong Coupling Phenomena on the Noncommutative Plane
We study strong coupling phenomena in U(1) gauge theory on the
non-commutative plane. To do so, we make use of a T-dual description in terms
of an limit of U(N) gauge theory on a commutative torus. The
magnetic flux on this torus is taken to be , while the area scales like
1/N, keeping fixed. With a few assumptions, we argue that the
speed of high frequency light in pure non-commutative QED is modified in the
non-commutative directions by the factor , where
is the non-commutative parameter. If charged flavours are included,
there is an upper bound on the momentum of a photon propagating in the
non-commutative directions, beyond which it is unstable against production of
charged pairs. We also discuss a particular limit of pure
non-commutative QED which is T-dual to a more conventional limit
with fixed. In the non-commutative description, this limit gives rise to
an exotic theory of open strings.Comment: 24 pages, latex, 2 figures, corrected typo in eqn 6.
Monopoles, noncommutative gauge theories in the BPS limit and some simple gauge groups
For three conspicuous gauge groups, namely, SU(2), SU(3) and SO(5), and at
first order in the noncommutative parameter matrix h\theta^{\mu\nu}, we
construct smooth monopole --and, some two-monopole-- fields that solve the
noncommutative Yang-Mills-Higgs equations in the BPS limit and that are formal
power series in h\theta^{\mu\nu}. We show that there exist noncommutative BPS
(multi-)monopole field configurations that are formal power series in
h\theta^{\mu\nu} if, and only if, two a priori free parameters of the
Seiberg-Witten map take very specific values. These parameters, that are not
associated to field redefinitions nor to gauge transformations, have thus
values that give rise to sharp physical effects.Comment: 30 pages, no figure
On the Nonperturbative Consistency of String Theory
An infinite number of distinct matrix models reproduce the perturbation
theory of string theory. Due to constraints of causality, however, we
argue that none of the existing constructions gives a consistent
nonperturbative definition of the string.Comment: 10 pages, 2 figures, LaTeX (author's name added
Properties of the conditionally filtered equations: Conservation, normal modes, and variational formulation
This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record.Conditionally filtered equations have recently been proposed as a basis for modelling
the atmospheric boundary layer and convection. Conditional filtering decomposes the
fluid into a number of categories or components, such as convective updrafts and the
background environment, and derives governing equations for the dynamics of each
component. Because of the novelty and unfamiliarity of these equations, it is important
to establish some of their physical and mathematical properties, and to examine whether
their solutions might behave in counter-intuitive or even unphysical ways. It is also
important to understand the properties of the equations in order to develop suitable
numerical solution methods. The conditionally filtered equations are shown to have
conservation laws for mass, entropy, momentum or axial angular momentum, energy,
and potential vorticity. The normal modes of the conditionally filtered equations include
the usual acoustic, inertio-gravity, and Rossby modes of the standard compressible Euler
equations. In addition, they posses modes with different perturbations in the different
fluid components that resemble gravity modes and inertial modes but with zero pressure
perturbation. These modes make no contribution to the total filter-scale fluid motion,
and their amplitude diminishes as the filter scale diminishes. Finally, it is shown that
the conditionally filtered equations have a natural variational formulation, which can be
used as a basis for systematically deriving consistent approximations.We are grateful to two anonymous reviewers for their constructive comments on an earlier version of this paper. This work was funded by the Natural Environment Research Council under grant NE/N013123/1 as part of the ParaCon programme
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