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