4,350 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
Syntactic characterization in Lisp of the polynomial complexity classes and hierarchy
The definition of a class C of functions is syntactic if membership to C can be decided from the construction of its elements. Syntactic
characterizations of PTIMEF, of PSPACEF, of the polynomial hierarchy PH, and of its subclasses Delta^p_n are presented. They are obtained by
progressive restrictions of recursion in Lisp, and may be regarded as predicative according to a foundational point raised by Leivant
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
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
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
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
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
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
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
Black-holes, topological strings and large N phase transitions
The counting of microstates of BPS black-holes on local Calabi-Yau of the
form is explored
by computing the partition function of q-deformed Yang-Mills theory on .
We obtain, at finite , the instanton expansion of the gauge theory. It can
be written exactly as the partition function for U(N) Chern-Simons gauge theory
on a Lens space, summed over all non-trivial vacua, plus a tower of
non-perturbative instanton contributions. In the large limit we find a
peculiar phase structure in the model. At weak string coupling the theory
reduces to the trivial sector and the topological string partition function on
the resolved conifold is reproduced in this regime. At a certain critical
point, instantons are enhanced and the theory undergoes a phase transition into
a strong coupling regime. The transition from the strong coupling phase to the
weak coupling phase is of third order.Comment: 16 pages, 3 figures; Invited talk given at QG05, Cala Gonone (Italy),
September 200
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