2,681 research outputs found
On the Hochschild homology of open Frobenius algebras
We prove that the shifted Hochschild chain complex of a
symmetric open Frobenius algebra of degree has a natural homotopy
coBV-algebra structure. As a consequence and
are respectively coBV and BV algebras. The underlying
coalgebra and algebra structure may not be resp. counital and unital. We also
introduce a natural homotopy BV-algebra structure on hence a
BV-structure on . Moreover we prove that the product and
coproduct on satisfy the Frobenius compatibility condition i.e.
is an open Frobenius algebras. If is commutative, we also
introduce a natural BV structure on the shifted relative Hochschild homology
. We conjecture that the product of this BV
structure is identical to the Goresky-Hingston\cite{GH} product on the
cohomology of free loop spaces when is a commutative cochain algebra model
for .Comment: Many corrections have been made and the signs are now given explicil
On algebraic structures of the Hochschild complex
We first review various known algebraic structures on the Hochschild
(co)homology of a differential graded algebras under weak Poincar{\'e} duality
hypothesis, such as Calabi-Yau algebras, derived Poincar{\'e} duality algebras
and closed Frobenius algebras. This includes a BV-algebra structure on
or , which in the latter case is an extension of
the natural Gerstenhaber structure on . As an example, after proving
that the chain complex of the Moore loop space of a manifold is a
CY-algebra and using Burghelea-Fiedorowicz-Goodwillie theorem we obtain a
BV-structure on the homology of the free space. In Sections 6 we prove that
these BV/coBVstructures can be indeed defined for the Hochschild homology of a
symmetric open Frobenius DG-algebras. In particular we prove that the
Hochschild homology and cohomology of a symmetric open Frobenius algebra is a
BV and coBV-algebra. In Section 7 we exhibit a BV structure on the shifted
relative Hochschild homology of a symmetric commutative Frobenius algebra. The
existence of a BV-structure on the relative Hochschild homology was expected in
the light of Chas-Sullivan and Goresky-Hingston results for free loop spaces.
In Section 8 we present an action of Sullivan diagrams on the Hochschild
(co)chain complex of a closed Frobenius DG-algebra. This recovers
Tradler-Zeinalian \cite{TZ} result for closed Froebenius algebras using the
isomorphism .Comment: This is the final version. Many improvements and corrections have
been made.To appear in Free Loop Spaces in Geometry and Topology, IRMA
Lectures in Mathematicsand Theoretical Physics, to be published by EMS-P
Generators of Dynamical Systems on Hilbert Modules
We characterize the generators of dynamical systems on Hilbert modules as
those generators of one-parameter groups of Banach space isometries which are
ternary derivations. We investigate in how far a similar condition can be
expressed in terms of generalized derivations
Charged Higgs production from polarized top-quark decay in the 2HDM considering the general-mass variable-flavor-number scheme
Charged Higgs bosons are predicted by some non-minimal Higgs
scenarios, such as models containing Higgs triplets and two-Higgs-doublet
models, so that the experimental observation of these bosons would indicate
physics beyond the Standard Model. In the present work, we introduce a new
channel to indirect search for the charged Higgses through the hadronic decay
of polarized top quarks where a top quark decays into a charged Higgs and
a bottom-flavored hadron via the hadronization process of the produced
bottom quark, . To obtain the energy
spectrum of produced -hadrons we present, for the first time, an analytical
expression for the corrections to the differential decay
width of the process in the presence of a massive b-quark
in the General-Mass Variable-Flavor-Number Scheme (GM-VFNS). We find that the
most reliable predictions for the B-hadron energy spectrum are made in the
GM-VFN scheme, specifically, when the Type-II 2HDM scenario is concerned
String topology of Poincare duality groups
Let G be a Poincare duality group of dimension n. For a given element g in G,
let C_g denote its centralizer subgroup. Let L_G be the graded abelian group
defined by (L_G)_p = oplus_{[g]}H_{p+n}(C_g) where the sum is taken over
conjugacy classes of elements in G. In this paper we construct a multiplication
on L_G directly in terms of intersection products on the centralizers. This
multiplication makes L_G a graded, associative, commutative algebra. When G is
the fundamental group of an aspherical, closed oriented n manifold M, then
(L_G)_* = H_{*+n}(LM), where LM is the free loop space of M. We show that the
product on L_G corresponds to the string topology loop product on H_*(LM)
defined by Chas and Sullivan.Comment: This is the version published by Geometry & Topology Monographs on 22
February 200
Next-to-leading order corrections to the spin-dependent energy spectrum of hadrons from polarized top quark decay in the general two Higgs doublet model
In recent years, searches for the light and heavy charged Higgs bosons have
been done by the ATLAS and the CMS collaborations at the Large Hadron Collider
(LHC) in proton-proton collision. Nevertheless, a definitive search is a
program that still has to be carried out at the LHC. The experimental
observation of charged Higgs bosons would indicate physics beyond the Standard
Model. In the present work, we study the scaled-energy distribution of
bottom-flavored mesons () inclusively produced in polarized top quark decays
into a light charged Higgs boson and a massless bottom quark at next-to-leading
order in the two-Higgs-doublet model; . This
spin-dependent energy distribution is studied in a specific helicity coordinate
system where the polarization vector of the top quark is measured with respect
to the direction of the Higgs momentum. The study of these energy distributions
could be considered as a new channel to search for the charged Higgs bosons at
the LHC. For our numerical analysis and phenomenological predictions, we
restrict ourselves to the unexcluded regions of the MSSM
parameter space determined by the recent results of the CMS \cite{CMS:2014cdp}
and ATLAS \cite{TheATLAScollaboration:2013wia} collaborations.Comment: 10 pages, 6 figures. arXiv admin note: text overlap with
arXiv:1611.0801
- …