121 research outputs found
One-dimensional Chern-Simons theory
We study a one-dimensional toy version of the Chern-Simons theory. We
construct its simplicial version which comprises features of a low-energy
effective gauge theory and of a topological quantum field theory in the sense
of Atiyah.Comment: 37 page
Formality theorems for Hochschild chains in the Lie algebroid setting
In this paper we prove Lie algebroid versions of Tsygan's formality
conjecture for Hochschild chains both in the smooth and holomorphic settings.
In the holomorphic setting our result implies a version of Tsygan's formality
conjecture for Hochschild chains of the structure sheaf of any complex manifold
and in the smooth setting this result allows us to describe quantum traces for
an arbitrary Poisson Lie algebroid. The proofs are based on the use of
Kontsevich's quasi-isomorphism for Hochschild cochains of R[[y_1,...,y_d]],
Shoikhet's quasi-isomorphism for Hochschild chains of R[[y_1,...,y_d]], and
Fedosov's resolutions of the natural analogues of Hochschild (co)chain
complexes associated with a Lie algebroid.Comment: 40 pages, no figure
Hypercommutative operad as a homotopy quotient of BV
We give an explicit formula for a quasi-isomorphism between the operads
Hycomm (the homology of the moduli space of stable genus 0 curves) and
BV/ (the homotopy quotient of Batalin-Vilkovisky operad by the
BV-operator). In other words we derive an equivalence of Hycomm-algebras and
BV-algebras enhanced with a homotopy that trivializes the BV-operator.
These formulas are given in terms of the Givental graphs, and are proved in
two different ways. One proof uses the Givental group action, and the other
proof goes through a chain of explicit formulas on resolutions of Hycomm and
BV. The second approach gives, in particular, a homological explanation of the
Givental group action on Hycomm-algebras.Comment: minor corrections added, to appear in Comm.Math.Phy
Formality theorems for Hochschild complexes and their applications
We give a popular introduction to formality theorems for Hochschild complexes
and their applications. We review some of the recent results and prove that the
truncated Hochschild cochain complex of a polynomial algebra is non-formal.Comment: Submitted to proceedings of Poisson 200
Morita Equivalence, Picard Groupoids and Noncommutative Field Theories
In this article we review recent developments on Morita equivalence of star
products and their Picard groups. We point out the relations between
noncommutative field theories and deformed vector bundles which give the Morita
equivalence bimodules.Comment: Latex2e, 10 pages. Conference Proceeding for the Sendai Meeting 2002.
Some typos fixe
Interpolating Coherent States for Heisenberg-Weyl and Single-Photon SU(1,1) Algebras
New quantal states which interpolate between the coherent states of the
Heisenberg_Weyl and SU(1,1) algebras are introduced. The interpolating states
are obtained as the coherent states of a closed and symmetric algebra which
interpolates between the two algebras. The overcompleteness of the
interpolating coherent states is established. Differential operator
representations in suitable spaces of entire functions are given for the
generators of the algebra. A nonsymmetric set of operators to realize the
Heisenberg-Weyl algebra is provided and the relevant coherent states are
studied.Comment: 13 pages nd 5 ps figure
On the Open-Closed B-Model
We study the coupling of the closed string to the open string in the
topological B-model. These couplings can be viewed as gauge invariant
observables in the open string field theory, or as deformations of the
differential graded algebra describing the OSFT. This is interpreted as an
intertwining map from the closed string sector to the deformation (Hochschild)
complex of the open string algebra. By an explicit calculation we show that
this map induces an isomorphism of Gerstenhaber algebras on the level of
cohomology. Reversely, this can be used to derive the closed string from the
open string. We shortly comment on generalizations to other models, such as the
A-model.Comment: LaTeX, 48 pages. Citation adde
Effective Batalin--Vilkovisky theories, equivariant configuration spaces and cyclic chains
Kontsevich's formality theorem states that the differential graded Lie
algebra of multidifferential operators on a manifold M is
L-infinity-quasi-isomorphic to its cohomology. The construction of the
L-infinity map is given in terms of integrals of differential forms on
configuration spaces of points in the upper half-plane. Here we consider
configuration spaces of points in the disk and work equivariantly with respect
to the rotation group. This leads to considering the differential graded Lie
algebra of multivector fields endowed with a divergence operator. In the case
of R^d with standard volume form, we obtain an L-infinity morphism of modules
over this differential graded Lie algebra from cyclic chains of the algebra of
functions to multivector fields. As a first application we give a construction
of traces on algebras of functions with star-products associated with
unimodular Poisson structures. The construction is based on the
Batalin--Vilkovisky quantization of the Poisson sigma model on the disk and in
particular on the treatment of its zero modes.Comment: 27 page
Dynamic changes in eIF4F-mRNA interactions revealed by global analyses of environmental stress responses
BACKGROUND: Translation factors eIF4E and eIF4G form eIF4F, which interacts with the messenger RNA (mRNA) 5' cap to promote ribosome recruitment and translation initiation. Variations in the association of eIF4F with individual mRNAs likely contribute to differences in translation initiation frequencies between mRNAs. As translation initiation is globally reprogrammed by environmental stresses, we were interested in determining whether eIF4F interactions with individual mRNAs are reprogrammed and how this may contribute to global environmental stress responses. RESULTS: Using a tagged-factor protein capture and RNA-sequencing (RNA-seq) approach, we have assessed how mRNA associations with eIF4E, eIF4G1 and eIF4G2 change globally in response to three defined stresses that each cause a rapid attenuation of protein synthesis: oxidative stress induced by hydrogen peroxide and nutrient stresses caused by amino acid or glucose withdrawal. We find that acute stress leads to dynamic and unexpected changes in eIF4F-mRNA interactions that are shared among each factor and across the stresses imposed. eIF4F-mRNA interactions stabilised by stress are predominantly associated with translational repression, while more actively initiating mRNAs become relatively depleted for eIF4F. Simultaneously, other mRNAs are insulated from these stress-induced changes in eIF4F association. CONCLUSION: Dynamic eIF4F-mRNA interaction changes are part of a coordinated early translational control response shared across environmental stresses. Our data are compatible with a model where multiple mRNA closed-loop complexes form with differing stability. Hence, unexpectedly, in the absence of other stabilising factors, rapid translation initiation on mRNAs correlates with less stable eIF4F interactions
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