On the Hochschild homology of open Frobenius algebras

We prove that the shifted Hochschild chain complex $C\_*(A,A)[m]$ of a symmetric open Frobenius algebra $A$ of degree $m$ has a natural homotopy coBV-algebra structure. As a consequence $HH\_*(A,A)[m]$ and $HH^*(A,A^\vee)[-m]$ 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 $C\_*(A,A)[m]$ hence a BV-structure on $HH\_*(A,A)[m]$. Moreover we prove that the product and coproduct on $HH\_*(A,A)[m]$ satisfy the Frobenius compatibility condition i.e. $HH\_*(A,A)[m]$ is an open Frobenius algebras. If $A$ is commutative, we also introduce a natural BV structure on the shifted relative Hochschild homology $\widetilde{HH}\_*(A)[m-1]$. 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 $A$ is a commutative cochain algebra model for $M$.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 $HH^*(A,A^\vee)$ or $HH^*(A,A)$, which in the latter case is an extension of the natural Gerstenhaber structure on $HH^*(A,A)$. As an example, after proving that the chain complex of the Moore loop space of a manifold $M$ 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 $C^*(A ,A) \simeq C^*(A,A^\vee)$.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 $H^\pm$ 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 $H^+$ and a bottom-flavored hadron $B$ via the hadronization process of the produced bottom quark, $t(\uparrow)\rightarrow H^++b(\to B+jet)$. To obtain the energy spectrum of produced $B$-hadrons we present, for the first time, an analytical expression for the ${\cal O}(\alpha_s)$ corrections to the differential decay width of the process $t\rightarrow H^+b$ 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 ($B$) 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; $t(\uparrow)\to bH^+\to BH^++X$. 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 $m_{H^+}-\tan\beta$ 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