4,963 research outputs found
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
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
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
Stable divisorial gonality is in NP
Divisorial gonality and stable divisorial gonality are graph parameters,
which have an origin in algebraic geometry. Divisorial gonality of a connected
graph can be defined with help of a chip firing game on . The stable
divisorial gonality of is the minimum divisorial gonality over all
subdivisions of edges of .
In this paper we prove that deciding whether a given connected graph has
stable divisorial gonality at most a given integer belongs to the class NP.
Combined with the result that (stable) divisorial gonality is NP-hard by
Gijswijt, we obtain that stable divisorial gonality is NP-complete. The proof
consist of a partial certificate that can be verified by solving an Integer
Linear Programming instance. As a corollary, we have that the number of
subdivisions needed for minimum stable divisorial gonality of a graph with
vertices is bounded by for a polynomial
Assessment of malaria transmission changes in Africa, due to the climate impact of land use change using Coupled Model Intercomparison Project Phase 5 earth system models
Using mathematical modelling tools, we assessed the potential for land use change (LUC) associated with the Intergovernmental Panel on Climate Change low- and high-end emission scenarios (RCP2.6 and RCP8.5) to impact malaria transmission in Africa. To drive a spatially explicit, dynamical malaria model, data from the four available earth system models (ESMs) that contributed to the LUC experiment of the Fifth Climate Model Intercomparison Project are used. Despite the limited size of the ESM ensemble, stark differences in the assessment of how LUC can impact climate are revealed. In three out of four ESMs, the impact of LUC on precipitation and temperature over the next century is limited, resulting in no significant change in malaria transmission. However, in one ESM, LUC leads to increases in precipitation under scenario RCP2.6, and increases in temperature in areas of land use conversion to farmland under both scenarios. The result is a more intense transmission and longer transmission seasons in the southeast of the continent, most notably in Mozambique and southern Tanzania. In contrast, warming associated with LUC in the Sahel region reduces risk in this model, as temperatures are already above the 25-30°C threshold at which transmission peaks. The differences between the ESMs emphasise the uncertainty in such assessments. It is also recalled that the modelling framework is unable to adequately represent local-scale changes in climate due to LUC, which some field studies indicate could be significant
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
A predicative and decidable characterization of the polynomial classes of languages
Characterizations of PTIME, PSPACE, the polynomial hierarchy and its elements are given, which are decidable (membership can be decided by syntactic inspection to the constructions), predicative (according to points of view by Leivant and others), and are obtained by means of increasing restrictions to course-of-values recursion on trees (represented in a dialect of Lisp). (C) 2001 Elsevier Science B.V. All rights reserved
Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED
We re-examine the perturbative properties of four-dimensional non-commutative
QED by extending the pinch techniques to the theta-deformed case. The explicit
independence of the pinched gluon self-energy from gauge-fixing parameters, and
the absence of unphysical thresholds in the resummed propagators permits a
complete check of the optical theorem for the off-shell two-point function. The
known anomalous (tachyonic) dispersion relations are recovered within this
framework, as well as their improved version in the (softly broken) SUSY case.
These applications should be considered as a first step in constructing
gauge-invariant truncations of the Schwinger-Dyson equations in the
non-commutative case. An interesting result of our formalism appears when
considering the theory in two dimensions: we observe a finite gauge-invariant
contribution to the photon mass because of a novel incarnation of IR/UV mixing,
which survives the commutative limit when matter is present.Comment: 30 pages, 2 eps figure, uses axodraw. Citations adde
Factors Associated with the Diversification of the Gut Microbial Communities within Chimpanzees from Gombe National Park.
The gastrointestinal tract harbors large and diverse populations of bacteria that vary among individuals and within individuals over time. Numerous internal and external factors can influence the contents of these microbial communities, including diet, geography, physiology, and the extent of contact among hosts. To investigate the contributions of such factors to the variation and changes in gut microbial communities, we analyzed the distal gut microbiota of individual chimpanzees from two communities in Gombe National Park, Tanzania. These samples, which were derived from 35 chimpanzees, many of whom have been monitored for multiple years, provide an unusually comprehensive longitudinal depth for individuals of known genetic relationships. Although the composition of the great-ape microbiota has been shown to codiversify with host species, indicating that host genetics and phylogeny have played a major role in its differentiation over evolutionary timescales, the geneaological relationships of individual chimpanzees did not coincide with the similarity in their gut microbial communities. However, the inhabitants from adjacent chimpanzee communities could be distinguished based on the contents of their gut microbiota. Despite the broad similarity of community members, as would be expected from shared diet or interactions, long-term immigrants to a community often harbored the most distinctive gut microbiota, suggesting that individuals retain hallmarks of their previous gut microbial communities for extended periods. This pattern was reinforced in several chimpanzees sampled over long temporal scales, in which the major constituents of the gut microbiota were maintained for nearly a decade
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