11 research outputs found
Conformal windows of SP(2N) and SO(N) gauge theories from topological excitations on R3 * S1
We derive an estimate of the lower boundary of the conformal window of SP(2N)
and SO(N) gauge theories with fermionic matter in several different
representations. We calculate the index of topological excitations for these
groups on the manifold R3 * S1, from which we deduce the scale of the
generation of the mass gap of the theory. This is then used to approximate the
critical value of the number of species for the onset of conformality on R4. We
also provide a detailed comparison with other estimates of the conformal
window.Comment: 23 pages, 4 figures, 7 tables; updated results, added comparisons,
references adde
Index theorem for topological excitations on R^3 * S^1 and Chern-Simons theory
We derive an index theorem for the Dirac operator in the background of
various topological excitations on an R^3 \times S^1 geometry. The index
theorem provides more refined data than the APS index for an instanton on R^4
and reproduces it in decompactification limit. In the R^3 limit, it reduces to
the Callias index theorem. The index is expressed in terms of topological
charge and the eta-invariant associated with the boundary Dirac operator.
Neither topological charge nor eta-invariant is typically an integer, however,
the non-integer parts cancel to give an integer-valued index. Our derivation is
based on axial current non-conservation--an exact operator identity valid on
any four-manifold--and on the existence of a center symmetric, or approximately
center symmetric, boundary holonomy (Wilson line). We expect the index theorem
to usefully apply to many physical systems of interest, such as low temperature
(large S^1, confined) phases of gauge theories, center stabilized Yang-Mills
theories with vector-like or chiral matter (at S^1 of any size), and
supersymmetric gauge theories with supersymmetry-preserving boundary conditions
(also at any S^1). In QCD-like and chiral gauge theories, the index theorem
should shed light into the nature of topological excitations responsible for
chiral symmetry breaking and the generation of mass gap in the gauge sector. We
also show that imposing chirally-twisted boundary condition in gauge theories
with fermions induces a Chern-Simons term in the infrared. This suggests that
some QCD-like gauge theories should possess components with a topological
Chern-Simons phase in the small S^1 regime.Comment: 29 pages, refs added, published versio
Chiral gauge dynamics and dynamical supersymmetry breaking
We study the dynamics of a chiral SU(2) gauge theory with a Weyl fermion in
the I=3/2 representation and of its supersymmetric generalization. In the
former, we find a new and exotic mechanism of confinement, induced by
topological excitations that we refer to as magnetic quintets. The
supersymmetric version was examined earlier in the context of dynamical
supersymmetry breaking by Intriligator, Seiberg, and Shenker, who showed that
if this gauge theory confines at the origin of moduli space, one may break
supersymmetry by adding a tree level superpotential. We examine the dynamics by
deforming the theory on S^1 x R^3, and show that the infrared behavior of this
theory is an interacting CFT at small S^1. We argue that this continues to hold
at large S^1, and if so, that supersymmetry must remain unbroken. Our methods
also provide the microscopic origin of various superpotentials in SQCD on S^1 x
R^3 - which were previously obtained by using symmetry and holomorphy - and
resolve a long standing interpretational puzzle concerning a flux operator
discovered by Affleck, Harvey, and Witten. It is generated by a topological
excitation, a "magnetic bion", whose stability is due to fermion pair exchange
between its constituents. We also briefly comment on composite monopole
operators as leading effects in two dimensional anti-ferromagnets.Comment: 30 pages, 5 figure
The generalized Robinson-Foulds metric
The Robinson-Foulds (RF) metric is arguably the most widely used measure of
phylogenetic tree similarity, despite its well-known shortcomings: For example,
moving a single taxon in a tree can result in a tree that has maximum distance
to the original one; but the two trees are identical if we remove the single
taxon. To this end, we propose a natural extension of the RF metric that does
not simply count identical clades but instead, also takes similar clades into
consideration. In contrast to previous approaches, our model requires the
matching between clades to respect the structure of the two trees, a property
that the classical RF metric exhibits, too. We show that computing this
generalized RF metric is, unfortunately, NP-hard. We then present a simple
Integer Linear Program for its computation, and evaluate it by an
all-against-all comparison of 100 trees from a benchmark data set. We find that
matchings that respect the tree structure differ significantly from those that
do not, underlining the importance of this natural condition.Comment: Peer-reviewed and presented as part of the 13th Workshop on
Algorithms in Bioinformatics (WABI2013
Geometric tree kernels: Classification of COPD from airway tree geometry
Methodological contributions: This paper introduces a family of kernels for
analyzing (anatomical) trees endowed with vector valued measurements made along
the tree. While state-of-the-art graph and tree kernels use combinatorial
tree/graph structure with discrete node and edge labels, the kernels presented
in this paper can include geometric information such as branch shape, branch
radius or other vector valued properties. In addition to being flexible in
their ability to model different types of attributes, the presented kernels are
computationally efficient and some of them can easily be computed for large
datasets (N of the order 10.000) of trees with 30-600 branches. Combining the
kernels with standard machine learning tools enables us to analyze the relation
between disease and anatomical tree structure and geometry. Experimental
results: The kernels are used to compare airway trees segmented from low-dose
CT, endowed with branch shape descriptors and airway wall area percentage
measurements made along the tree. Using kernelized hypothesis testing we show
that the geometric airway trees are significantly differently distributed in
patients with Chronic Obstructive Pulmonary Disease (COPD) than in healthy
individuals. The geometric tree kernels also give a significant increase in the
classification accuracy of COPD from geometric tree structure endowed with
airway wall thickness measurements in comparison with state-of-the-art methods,
giving further insight into the relationship between airway wall thickness and
COPD. Software: Software for computing kernels and statistical tests is
available at http://image.diku.dk/aasa/software.php.Comment: 12 page
Calorons, Nahm's equations on S^1 and bundles over P^1xP^1
The moduli space of solutions to Nahm's equations of rank (k,k+j) on the
circle, and hence, of SU(2) calorons of charge (k,j), is shown to be equivalent
to the moduli of holomorphic rank 2 bundles on P^1xP^1 trivialized at infinity
with c_2=k and equipped with a flag of degree j along P^1x{0}. An explicit
matrix description of these spaces is given by a monad constructio
Conformality or confinement: (IR)relevance of topological excitations
We study aspects of the conformality to confinement transition for
non-supersymmetric Yang-Mills theories with fermions in arbitrary chiral or
vectorlike representations. We use the presence or absence of mass gap for
gauge fluctuations as an identifier of the infrared behavior. Present-day
understanding does not allow the mass gap for gauge fluctuations to be computed
on R*4. However, recent progress allows its non-perturbative computation on
R*3xS*1 by using either the twisted partition function or deformation theory,
for a range of S*1 sizes depending on the theory. For small number of fermions,
Nf, we show that the mass gap increases with increasing radius, due to the
non-dilution of monopoles and bions, the topological excitations relevant for
confinement on R*3xS*1. For sufficiently large Nf, we show that the mass gap
decreases with increasing radius. In a class of theories, we claim that the
decompactification limit can be taken while remaining within the region of
validity of semi-classical techniques, giving the first examples of
semiclassically solvable Yang-Mills theories at any size S*1. For general
non-supersymmetric vectorlike or chiral theories, we conjecture that the change
in the behavior of the mass gap on R*3xS*1 as a function of the radius occurs
near the lower boundary of the conformal window and give non-perturbative
estimates of its value. For vectorlike theories, we compare our estimates of
the conformal window with existing lattice results, truncations of the
Schwinger-Dyson equations, NSVZ beta function-inspired estimates, and degree of
freedom counting criteria. For multi-generation chiral gauge theories, to the
best of our knowledge, our estimates of the conformal window are the only known
ones.Comment: 40 pages, 3 figures; modified various comments, reference adde
Adjoint fermion zero-modes for SU(N) calorons
We derive analytic formulas for the zero-modes of the Dirac equation in the
adjoint representation in the background field of Q=1 SU(N) calorons. Solutions
with various boundary conditions are obtained, including the physically most
relevant cases of periodic and antiperiodic ones. The latter are essential
ingredients in a semiclassical treatment of finite temperature supersymmetric
Yang-Mills theory. A detailed discussion of adjoint zero-modes in several other
contexts is also presented.Comment: 40 latex pages and 5 eps figure
A sparse Bayesian hierarchical vector autoregressive model for microbial dynamics in a wastewater treatment plant
Proper function of a wastewater treatment plant (WWTP) relies on maintaining a delicate balance between a multitude of competing microorganisms. Gaining a detailed understanding of the complex network of interactions therein is essential to maximising not only current operational efficiencies, but also for the effective design of new treatment technologies. Metagenomics offers an insight into these dynamic systems through the analysis of the microbial DNA sequences present. Unique taxa are deduced through sequence clustering to form operational taxonomic units (OTUs), with per-taxa abundance estimates obtained from corresponding sequence counts. The data in this study comprise weekly OTU counts from an activated sludge (AS) tank of a WWTP along with corresponding measurements of chemical and environmental (CE) covariates. Directly fitting a model to the OTU data is incredibly challenging because of the high dimensionality and sparsity of the observations. The first step is therefore to aggregate the OTUs into twelve microbial communities or “bins” using a seasonal phase-based clustering approach. The mean abundances in the twelve bins are assumed to vary over time according to a multivariate linear regression on the CE covariates. Deviations from the mean are then modelled using a vector autoregressive (VAR) model of order one, which is a linear approximation to the commonly used generalised Lotka-Volterra (gLV) model. Sparsity is assumed in the interactions between microbial communities by carrying out inference in a hierarchical Bayesian framework which uses a shrinkage prior for the autoregressive coefficient matrix of the VAR model. Different shrinkage priors are explored by analysing simulated data sets before selecting the regularised horseshoe prior for the biological application. It is found that ammonia and chemical oxygen demand have a positive relationship with several bins and pH has a positive relationship with one bin. These results are supported by findings in the biological literature. Several negative interactions are also identified. These novel biological findings suggest OTUs in different bins may be competing for resources and that these relationships are complex. Although simpler than a gLV model, the VAR model is still able to offer valuable insight into the microbial dynamics of the WWTP