8,906 research outputs found
Limit Cycles and Conformal Invariance
There is a widely held belief that conformal field theories (CFTs) require
zero beta functions. Nevertheless, the work of Jack and Osborn implies that the
beta functions are not actually the quantites that decide conformality, but
until recently no such behavior had been exhibited. Our recent work has led to
the discovery of CFTs with nonzero beta functions, more precisely CFTs that
live on recurrent trajectories, e.g., limit cycles, of the beta-function vector
field. To demonstrate this we study the S function of Jack and Osborn. We use
Weyl consistency conditions to show that it vanishes at fixed points and agrees
with the generator Q of limit cycles on them. Moreover, we compute S to third
order in perturbation theory, and explicitly verify that it agrees with our
previous determinations of Q. A byproduct of our analysis is that, in
perturbation theory, unitarity and scale invariance imply conformal invariance
in four-dimensional quantum field theories. Finally, we study some properties
of these new, "cyclic" CFTs, and point out that the a-theorem still governs the
asymptotic behavior of renormalization-group flows.Comment: 31 pages, 4 figures. Expanded introduction to make clear that cycles
discussed in this work are not associated with unitary theories that are
scale but not conformally invarian
Task-based Augmented Contour Trees with Fibonacci Heaps
This paper presents a new algorithm for the fast, shared memory, multi-core
computation of augmented contour trees on triangulations. In contrast to most
existing parallel algorithms our technique computes augmented trees, enabling
the full extent of contour tree based applications including data segmentation.
Our approach completely revisits the traditional, sequential contour tree
algorithm to re-formulate all the steps of the computation as a set of
independent local tasks. This includes a new computation procedure based on
Fibonacci heaps for the join and split trees, two intermediate data structures
used to compute the contour tree, whose constructions are efficiently carried
out concurrently thanks to the dynamic scheduling of task parallelism. We also
introduce a new parallel algorithm for the combination of these two trees into
the output global contour tree. Overall, this results in superior time
performance in practice, both in sequential and in parallel thanks to the
OpenMP task runtime. We report performance numbers that compare our approach to
reference sequential and multi-threaded implementations for the computation of
augmented merge and contour trees. These experiments demonstrate the run-time
efficiency of our approach and its scalability on common workstations. We
demonstrate the utility of our approach in data segmentation applications
Characters of graded parafermion conformal field theory
The graded parafermion conformal field theory at level k is a close cousin of
the much-studied Z_k parafermion model. Three character formulas for the graded
parafermion theory are presented, one bosonic, one fermionic (both previously
known) and one of spinon type (which is new). The main result of this paper is
a proof of the equivalence of these three forms using q-series methods combined
with the combinatorics of lattice paths. The pivotal step in our approach is
the observation that the graded parafermion theory -- which is equivalent to
the coset osp(1,2)_k/ u(1) -- can be factored as (osp(1,2)_k/ su(2)_k) x
(su(2)_k/ u(1)), with the two cosets on the right equivalent to the minimal
model M(k+2,2k+3) and the Z_k parafermion model, respectively. This
factorisation allows for a new combinatorial description of the graded
parafermion characters in terms of the one-dimensional configuration sums of
the (k+1)-state Andrews--Baxter--Forrester model.Comment: 36 page
Is the decoherence of a system the result of its interaction with the environment?
According to a usual reading, decoherence is a process resulting from the
interaction between a small system and its large environment where information
and energy are dissipated. The particular models treated in the literature on
the subject reinforce this idea since, in general, the behavior of a particle
immersed in a large "bath" composed by many particles is studied. The aim of
this letter is to warn against this usual simplified reading. By means of the
analysis of a well-known model, we will show that decoherence may occur in a
system interacting with an environment consisting of only one particle.Comment: 4 Pages, 5 Figure
Neutron stars with hyperon cores: stellar radii and EOS near nuclear density
The existence of 2 Msun pulsars puts very strong constraints on the equation
of state (EOS) of neutron stars (NSs) with hyperon cores, which can be
satisfied only by special models of hadronic matter. The radius-mass relation
for these models is sufficiently specific that it could be subjected to an
observational test with future X-ray observatories. We want to study the impact
of the presence of hyperon cores on the radius-mass relation for NS. We aim to
find out how, and for which particular stellar mass range, a specific relation
R(M), where M is the gravitational mass, and R is the circumferential radius,
is associated with the presence of a hyperon core.
We consider a set of 14 theoretical EOS of dense matter, based on the
relativistic mean-field (RMF) approximation, allowing for the presence of
hyperons in NSs. We seek correlations between R(M) and the stiffness of the EOS
below the hyperon threshold needed to pass the 2 Msun test. For NS masses
1.013km, because of a very stiff pre-hyperon segment of
the EOS. At nuclear density, the pressure is significantly higher than a robust
upper bound obtained recently using chiral effective field theory.
If massive NSs do have a sizable hyperon core, then according to current
models the radii for M=1.0-1.6 Msun are necessarily >13km. If, on the contrary,
a NS with a radius R<12 km is observed in this mass domain, then sizable
hyperon cores in NSs, as we model them now, are ruled out. Future X-ray
missions with <5% precision for a simultaneous M and R measurement will have
the potential to solve the problem with observations of NSs. Irrespective of
this observational test, present EOS allowing for hyperons that fulfill
condition M_max>2 Msun yield a pressure at nuclear density that is too high
relative to up-to-date microscopic calculations of this quantity.Comment: 10 pages, 10 figures, published in A&
Limit Cycles in Four Dimensions
We present an example of a limit cycle, i.e., a recurrent flow-line of the
beta-function vector field, in a unitary four-dimensional gauge theory. We thus
prove that beta functions of four-dimensional gauge theories do not produce
gradient flows. The limit cycle is established in perturbation theory with a
three-loop calculation which we describe in detail.Comment: 12 pages, 1 figure. Significant revision of the interpretation of our
result. Improved description of three-loop calculatio
Rotating neutron stars with exotic cores: masses, radii, stability
A set of theoretical mass-radius relations for rigidly rotating neutron stars
with exotic cores, obtained in various theories of dense matter, is reviewed.
Two basic observational constraints are used: the largest measured rotation
frequency (716 Hz) and the maximum measured mass (). Present status
of measuring the radii of neutron stars is described. The theory of rigidly
rotating stars in general relativity is reviewed and limitations of the slow
rotation approximation are pointed out. Mass-radius relations for rotating
neutron stars with hyperon and quark cores are illustrated using several
models. Problems related to the non-uniqueness of the crust-core matching are
mentioned. Limits on rigid rotation resulting from the mass-shedding
instability and the instability with respect to the axisymmetric perturbations
are summarized. The problem of instabilities and of the back-bending phenomenon
are discussed in detail. Metastability and instability of a neutron star core
in the case of a first-order phase transition, both between pure phases, and
into a mixed-phase state, are reviewed. The case of two disjoint families
(branches) of rotating neutron stars is discussed and generic features of
neutron-star families and of core-quakes triggered by the instabilities are
considered.Comment: Matches published version. Minor modifications and reference adde
Recommended from our members
Dissociating visuo-spatial and verbal working memory: Itâs all in the features
Echoing many of the themes of the seminal work of Atkinson and Shiffrin (1968), this paper uses the Feature Model (Nairne, 1988, 1990; Neath & Nairne, 1995) to account for performance in working memory tasks. The Brooks verbal and visuo-spatial matrix tasks were performed alone, with articulatory suppression, or with a spatial suppression task; the results produced the expected dissociation. We used Approximate Bayesian Computation techniques to fit the Feature Model to the data and showed that the similarity-based interference process implemented in the model accounted for the data patterns well. We then fit the model to data from Guérard and Tremblay (2008); the latter study produced a double dissociation while calling upon more typical order reconstruction tasks. Again, the model performed well. The findings show that a double dissociation can be modelled without appealing to separate systems for verbal and visuo-spatial processing. The latter findings are significant as the Feature Model had not been used to model this type of dissociation before; importantly, this is also the first time the model is quantitatively fit to data. For the demonstration provided here, modularity was unnecessary if two assumptions were made: (1) the main difference between spatial and verbal working memory tasks is the features that are encoded; (2) secondary tasks selectively interfere with primary tasks to the extent that both tasks involve similar features. It is argued that a feature-based view is more parsimonious (see Morey, 2018) and offers flexibility in accounting for multiple benchmark effects in the field
- âŠ