2,338 research outputs found
Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory
We study Chern-Simons theory on 3-manifolds that are circle-bundles over
2-dimensional surfaces and show that the method of Abelianisation,
previously employed for trivial bundles , can be adapted to
this case. This reduces the non-Abelian theory on to a 2-dimensional
Abelian theory on 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 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
's in the base of . At large 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
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 U(N) gauge
theories living on toric varieties, mainly of type
including 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 ÎČ -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
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