56 research outputs found
Path-integral invariants in abelian Chern-Simons theory
We consider the Chern-Simons gauge theory defined in a general closed
oriented 3-manifold ; the functional integration is used to compute the
normalized partition function and the expectation values of the link
holonomies. The nonperturbative path-integral is defined in the space of the
gauge orbits of the connections which belong to the various inequivalent
principal bundles over ; the different sectors of the configuration space
are labelled by the elements of the first homology group of and are
characterized by appropriate background connections. The gauge orbits of flat
connections, whose classification is also based on the homology group, control
the extent of the nonperturbative contributions to the mean values. The
functional integration is achieved in any 3-manifold , and the corresponding
path-integral invariants turn out to be strictly related with the abelian
Reshetikhin-Turaev surgery invariants
Topological gauge fixing
We implement the metric-independent Fock-Schwinger gauge in the abelian
quantum Chern-Simons field theory defined in . The expressions
of the various components of the propagator are determined. Although the gauge
field propagator differs from the Gauss linking density, we prove that its
integral along two oriented knots is equal to the linking number
Deligne-Beilinson cohomology and abelian links invariants
For the abelian Chern-Simons field theory, we consider the quantum functional
integration over the Deligne-Beilinson cohomology classes and we derive the
main properties of the observables in a generic closed orientable 3-manifold.
We present an explicit path-integral non-perturbative computation of the
Chern-Simons links invariants in the case of the torsion-free 3-manifolds
, and
An extension of the BF theory, Turaev-Viro invariant and Drinfeld center construction. Part I: Quantum fields, quantum currents and Pontryagin duality
In this first of a series of articles dedicated to natural extensions of the
U(1) BF theory, abelian Turaev-Viro (TV) construction and corresponding
Drinfeld center construction for any closed oriented smooth manifolds, we
present the mathematical background that will be used.Comment: 58 pages, 2 figure
Some remarks on topological 4d-gravity
We show that the method of S. Wu to study topological 4d-gravity can be
understood within a now standard method designed to produce equivariant
cohomology classes. Next, this general framework is applied to produce some
observables of the topological 4d-gravity.Comment: 10 pages, Late
Representatives of the Thom class of a vector bundle
After a review of several methods designed to produce equivariant cohomology
classes, we apply one introduced by Berline, Getzler and Vergne, to get a
family of representatives of the universal Thom class of a vector bundle.
Surprisingly, this family does not contain the representative given by
Matha\"{\i} and Quillen. However it contains a particularly simple and
symmetric representative that we construct explicitly.Comment: 19 pages, Latex, one reference and some related comments added;
submitted to Journal of Geometry and Physic
Three-manifold invariant from functional integration
We give a precise definition and produce a path-integral computation of the
normalized partition function of the abelian U(1) Chern-Simons field theory
defined in a general closed oriented 3-manifold. We use the Deligne-Beilinson
formalism, we sum over the inequivalent U(1) principal bundles over the
manifold and, for each bundle, we integrate over the gauge orbits of the
associated connection 1- forms. The result of the functional integration is
compared with the abelian U(1) Reshetikhin-Turaev surgery invariant
A Class of Topological Actions
We review definitions of generalized parallel transports in terms of
Cheeger-Simons differential characters. Integration formulae are given in terms
of Deligne-Beilinson cohomology classes. These representations of parallel
transport can be extended to situations involving distributions as is
appropriate in the context of quantized fields.Comment: 41 pages, no figure
Genetic fine mapping and genomic annotation defines causal mechanisms at type 2 diabetes susceptibility loci.
We performed fine mapping of 39 established type 2 diabetes (T2D) loci in 27,206 cases and 57,574 controls of European ancestry. We identified 49 distinct association signals at these loci, including five mapping in or near KCNQ1. 'Credible sets' of the variants most likely to drive each distinct signal mapped predominantly to noncoding sequence, implying that association with T2D is mediated through gene regulation. Credible set variants were enriched for overlap with FOXA2 chromatin immunoprecipitation binding sites in human islet and liver cells, including at MTNR1B, where fine mapping implicated rs10830963 as driving T2D association. We confirmed that the T2D risk allele for this SNP increases FOXA2-bound enhancer activity in islet- and liver-derived cells. We observed allele-specific differences in NEUROD1 binding in islet-derived cells, consistent with evidence that the T2D risk allele increases islet MTNR1B expression. Our study demonstrates how integration of genetic and genomic information can define molecular mechanisms through which variants underlying association signals exert their effects on disease
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