Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory

We study Chern-Simons theory on 3-manifolds $M$ that are circle-bundles over 2-dimensional surfaces $\Sigma$ and show that the method of Abelianisation, previously employed for trivial bundles $\Sigma \times S^1$, can be adapted to this case. This reduces the non-Abelian theory on $M$ to a 2-dimensional Abelian theory on $\Sigma$ which we identify with q-deformed Yang-Mills theory, as anticipated by Vafa et al. We compare and contrast our results with those obtained by Beasley and Witten using the method of non-Abelian localisation, and determine the surgery and framing presecription implicit in this path integral evaluation. We also comment on the extension of these methods to BF theory and other generalisations.Comment: 37 pages; v2: references adde

A Note on q-Deformed Two-Dimensional Yang-Mills and Open Topological Strings

In this note we make a test of the open topological string version of the OSV conjecture, proposed in hep-th/0504054, in the toric Calabi-Yau manifold $X= O(-3)\to\mathbf{P}^2$ with background D4-branes wrapped on Lagrangian submanifolds. The D-brane partition function reduces to an expectation value of some inserted operators of a q-deformed Yang-Mills theory living on a chain of $\mathbf{P}^1$'s in the base $\mathbf{P}^2$ of $X$. At large $N$ this partition function can be written as a sum over squares of chiral blocks, which are related to the open topological string amplitudes in the local $\mathbf{P}^2$ geometry with branes at both the outer and inner edges of the toric diagram. This is in agreement with the conjecture.Comment: 14 pages, 3 figure

Branes, Black Holes and Topological Strings on Toric Calabi-Yau Manifolds

We develop means of computing exact degerenacies of BPS black holes on toric Calabi-Yau manifolds. We show that the gauge theory on the D4 branes wrapping ample divisors reduces to 2D q-deformed Yang-Mills theory on necklaces of P^1's. As explicit examples we consider local P^2, P^1 x P^1 and A_k type ALE space times C. At large N the D-brane partition function factorizes as a sum over squares of chiral blocks, the leading one of which is the topological closed string amplitude on the Calabi-Yau. This is in complete agreement with the recent conjecture of Ooguri, Strominger and Vafa.Comment: 50 pages, 6 figures, harvma

Instanton on toric singularities and black hole countings

We compute the instanton partition function for ${\cal N}=4$ U(N) gauge theories living on toric varieties, mainly of type $\R^4/\Gamma_{p,q}$ including $A_{p-1}$ or O_{\PP_1}(-p) surfaces. The results provide microscopic formulas for the partition functions of black holes made out of D4-D2-D0 bound states wrapping four-dimensional toric varieties inside a Calabi-Yau. The partition function gets contributions from regular and fractional instantons. Regular instantons are described in terms of symmetric products of the four-dimensional variety. Fractional instantons are built out of elementary self-dual connections with no moduli carrying non-trivial fluxes along the exceptional cycles of the variety. The fractional instanton contribution agrees with recent results based on 2d SYM analysis. The partition function, in the large charge limit, reproduces the supergravity macroscopic formulae for the D4-D2-D0 black hole entropy.Comment: 29 pages, 3 fig Section 5 is improved by the inclusion of a detailed comparison between the instanton partition function and the D4-D2-D0 black hole entropy formula coming from supergravit

Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory

We study the WZW, Chern-Simons, and 2d qYM theories with gauge group U(N). The U(N) WZW model is only well-defined for odd level K, and this model is shown to exhibit level-rank duality in a much simpler form than that for SU(N). The U(N) Chern-Simons theory on Seifert manifolds exhibits a similar duality, distinct from the level-rank duality of SU(N) Chern-Simons theory on S^3. When q = e^{2 pi i/(N+K)}, the observables of the 2d U(N) qYM theory can be expressed as a sum over a finite subset of U(N) representations. When N and K are odd, the qYM theory exhibits N K duality, provided q = e^{2 pi i/(N+K)} and theta = 0 mod 2 pi /(N+K).Comment: 19 pages; v2: minor typo corrected, 1 paragraph added, published versio

Pinch Technique for Schwinger-Dyson equations

In the context of scalar QED we derive the pinch technique self-energies and vertices directly from the Schwinger-Dyson equations. After reviewing the perturbative construction, we discuss in detail the general methodology and the basic field-theoretic ingredients necessary for the completion of this task. The construction requires the simultaneous treatment of the equations governing the scalar self-energy and the fundamental interaction vertices. The resulting non-trivial rearrangement of terms generates dynamically the Schwinger-Dyson equations for the corresponding Green's functions of the background field method. The proof relies on the extensive use of the all-order Ward-identities satisfied by the full vertices of the theory and by the one-particle-irreducible kernels appearing in the usual skeleton expansion. The Ward identities for these latter quantities are derived formally, and several subtleties related to the structure of the multiparticle kernels are addressed. The general strategy for the generalization of the method in a non-Abelian context is briefly outlined, and some of the technical difficulties are discussed.Comment: 43 pages, 11 figures; title and abstract slightly modified, several clarifying discussions added; final version to match the one accpted for publication in JHE

SitePainter: a tool for exploring biogeographical patterns

As microbial ecologists take advantage of high-throughput analytical techniques to describe microbial communities across ever-increasing numbers of samples, the need for new analysis tools that reveal the intrinsic spatial patterns and structures of these populations is crucial. Here we present SitePainter, an interactive graphical tool that allows investigators to create or upload pictures of their study site, load diversity analyses data and display both diversity and taxonomy results in a spatial context. Features of SitePainter include: visualizing α -diversity, using taxonomic summaries; visualizing β -diversity, using results from multidimensional scaling methods; and animating relationships among microbial taxa or pathways overtime. SitePainter thus increases the visual power and ability to explore spatially explicit studies

Forensic analysis of the microbiome of phones and shoes

BACKGROUND: Microbial interaction between human-associated objects and the environments we inhabit may have forensic implications, and the extent to which microbes are shared between individuals inhabiting the same space may be relevant to human health and disease transmission. In this study, two participants sampled the front and back of their cell phones, four different locations on the soles of their shoes, and the floor beneath them every waking hour over a 2-day period. A further 89 participants took individual samples of their shoes and phones at three different scientific conferences. RESULTS: Samples taken from different surface types maintained significantly different microbial community structures. The impact of the floor microbial community on that of the shoe environments was strong and immediate, as evidenced by Procrustes analysis of shoe replicates and significant correlation between shoe and floor samples taken at the same time point. Supervised learning was highly effective at determining which participant had taken a given shoe or phone sample, and a Bayesian method was able to determine which participant had taken each shoe sample based entirely on its similarity to the floor samples. Both shoe and phone samples taken by conference participants clustered into distinct groups based on location, though much more so when an unweighted distance metric was used, suggesting sharing of low-abundance microbial taxa between individuals inhabiting the same space. CONCLUSIONS: Correlations between microbial community sources and sinks allow for inference of the interactions between humans and their environment. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s40168-015-0082-9) contains supplementary material, which is available to authorized users

Interpreting 16S metagenomic data without clustering to achieve sub-OTU resolution

The standard approach to analyzing 16S tag sequence data, which relies on clustering reads by sequence similarity into Operational Taxonomic Units (OTUs), underexploits the accuracy of modern sequencing technology. We present a clustering-free approach to multi-sample Illumina datasets that can identify independent bacterial subpopulations regardless of the similarity of their 16S tag sequences. Using published data from a longitudinal time-series study of human tongue microbiota, we are able to resolve within standard 97% similarity OTUs up to 20 distinct subpopulations, all ecologically distinct but with 16S tags differing by as little as 1 nucleotide (99.2% similarity). A comparative analysis of oral communities of two cohabiting individuals reveals that most such subpopulations are shared between the two communities at 100% sequence identity, and that dynamical similarity between subpopulations in one host is strongly predictive of dynamical similarity between the same subpopulations in the other host. Our method can also be applied to samples collected in cross-sectional studies and can be used with the 454 sequencing platform. We discuss how the sub-OTU resolution of our approach can provide new insight into factors shaping community assembly.Comment: Updated to match the published version. 12 pages, 5 figures + supplement. Significantly revised for clarity, references added, results not change