An Algebraic Construction of Boundary Quantum Field Theory

We build up local, time translation covariant Boundary Quantum Field Theory nets of von Neumann algebras ${\mathcal A_V}$ on the Minkowski half-plane M ₊ starting with a local conformal net ${\mathcal A}$ of von Neumann algebras on ${\mathbb R}$ and an element V of a unitary semigroup ${\mathcal E(\mathcal A)}$ associated with ${\mathcal A}$ . The case V?=?1 reduces to the net ${\mathcal A_+}$ considered by Rehren and one of the authors; if the vacuum character of ${\mathcal A}$ is summable, ${\mathcal A_V}$ is locally isomorphic to ${\mathcal A_+}$ . We discuss the structure of the semigroup ${\mathcal E(\mathcal A)}$ . By using a one-particle version of Borchers theorem and standard subspace analysis, we provide an abstract analog of the Beurling-Lax theorem that allows us to describe, in particular, all unitaries on the one-particle Hilbert space whose second quantization promotion belongs to ${\mathcal E(\mathcal A^{(0)})}$ with ${\mathcal A^{(0)}}$ the U(1)-current net. Each such unitary is attached to a scattering function or, more generally, to a symmetric inner function. We then obtain families of models via any Buchholz-Mack-Todorov extension of ${\mathcal A^{(0)}}$ . A further family of models comes from the Ising model.     

Optimal Paths for Symmetric Actions in the Unitary Group

Given a positive and unitarily invariant Lagrangian ${\mathcal{L}}$ defined in the algebra of matrices, and a fixed time interval ${[0,t_0]\subset\mathbb R}$ , we study the action defined in the Lie group of ${n\times n}$ unitary matrices ${\mathcal{U}(n)}$ by $$\mathcal{S}(\alpha)=\int_0^{t_0} \mathcal{L}(\dot\alpha(t))\,dt, $$ where ${\alpha:[0,t_0]\to\mathcal{U}(n)}$ is a rectifiable curve. We prove that the one-parameter subgroups of ${\mathcal{U}(n)}$ are the optimal paths, provided the spectrum of the exponent is bounded by π. Moreover, if ${\mathcal{L}}$ is strictly convex, we prove that one-parameter subgroups are the unique optimal curves joining given endpoints. Finally, we also study the connection of these results with unitarily invariant metrics in ${\mathcal{U}(n)}$ as well as angular metrics in the Grassmann manifold.     

Updated status of the global electroweak fit and constraints on new physics

We present an update of the Standard Model fit to electroweak precision data. We include newest experimental results on the top-quark mass, the W mass and width, and the Higgs-boson mass bounds from LEP, Tevatron and the LHC. We also include a new determination of the electromagnetic coupling strength at the Z pole. We find for the Higgs-boson mass $91^{+30}_{-23}~\mbox{GeV}$ and $120^{+12}_{-5}~\mbox{GeV}$ when not including and including the direct Higgs searches, respectively. From the latter fit we indirectly determine the W mass to be $(80.360^{+0.014}_{-0.013})~\mbox{GeV}$ . We exploit the data to determine experimental constraints on the oblique vacuum polarisation parameters, and confront these with predictions from the Standard Model (SM) and selected SM extensions. By fitting the oblique parameters to the electroweak data we derive allowed regions in the BSM parameter spaces. We revisit and consistently update these constraints for a fourth fermion generation, two Higgs doublet, inert Higgs and littlest Higgs models, models with large, universal or warped extra dimensions and technicolour. In most of the models studied a heavy Higgs boson can be made compatible with the electroweak precision data.     

The Lie–Rinehart Universal Poisson Algebra of Classical and Quantum Mechanics

The Lie–Rinehart algebra of a (connected) manifold ${\mathcal {M}}$ , defined by the Lie structure of the vector fields, their action and their module structure over ${C^\infty({\mathcal {M}})}$ , is a common, diffeomorphism invariant, algebra for both classical and quantum mechanics. Its (noncommutative) Poisson universal enveloping algebra ${\Lambda_{R}({\mathcal {M}})}$ , with the Lie–Rinehart product identified with the symmetric product, contains a central variable (a central sequence for non-compact ${{\mathcal {M}}}$ ) ${Z}$ which relates the commutators to the Lie products. Classical and quantum mechanics are its only factorial realizations, corresponding to Z  =  i z, z  =  0 and ${z = \hbar}$ , respectively; canonical quantization uniquely follows from such a general geometrical structure. For ${z =\hbar \neq 0}$ , the regular factorial Hilbert space representations of ${\Lambda_{R}({\mathcal{M}})}$ describe quantum mechanics on ${{\mathcal {M}}}$ . For z  =  0, if Diff( ${{\mathcal {M}}}$ ) is unitarily implemented, they are unitarily equivalent, up to multiplicity, to the representation defined by classical mechanics on ${{\mathcal {M}}}$ .     

Charged Higgs observability through associated production with W ± at a muon collider

The observability of a charged Higgs boson produced in association with a W boson at future muon colliders is studied. The analysis is performed within the MSSM framework. The charged Higgs is assumed to decay to $t\bar{b}We study $B_{s}^{0} \to J/\psi f_{0}(980)$ decays, the quark content of f ₀(980) and the mixing angle of f ₀(980) and ??(600). We calculate not only the factorizable contribution in the QCD factorization scheme but also the nonfactorizable hard spectator corrections in QCDF and pQCD approach. We get a result consistent with the experimental data of $B_{s}^{0} \to J/\psi f_{0}(980)$ and predict the branching ratio of $B_{s}^{0}$ ?CJ/???. We suggest two ways to determine f ₀?C?? mixing angle ??. Using the experimental measured branching ratio of $B_{s}^{0} \to J/\psi f_{0}(980)$ , we can get the f ₀?C?? mixing angle ?? with some theoretical uncertainties. We suggest another way to determine the f ₀?C?? mixing angle ?? using both experimental measured decay branching ratios $B_{s}^{0} \to J/\psi f_{0}(980) (\sigma)$ to avoid theoretical uncertainties.     

Inclusion relations for the spaces L(ℝ), \mathcal{H}\mathcal{K} (ℝ) ∩ \mathcal{B}\mathcal{V} (ℝ), and L 2(ℝ)

The inclusion relations for the spaces $ \mathcal{H}\mathcal{K} $ (I), L(I), $ \mathcal{H}\mathcal{K} $ (I) ∩ $ \mathcal{B}\mathcal{V} $ (I), and L ²(I) are found. On unbounded intervals, functions in $ \mathcal{H}\mathcal{K} $ (I) ∩ $ \mathcal{B}\mathcal{V} $ (I) need not be Lebesgue integrable.     

How to Add a Boundary Condition

Given a conformal QFT local net of von Neumann algebras ${\mathcal {B}_2}$ on the two-dimensional Minkowski spacetime with irreducible subnet ${\mathcal {A} \otimes \mathcal {A}}$ , where ${\mathcal {A}}$ is a completely rational net on the left/right light-ray, we show how to consistently add a boundary to ${\mathcal {B}_2}$ : we provide a procedure to construct a Boundary CFT net ${\mathcal {B}}$ of von Neumann algebras on the half-plane x >  0, associated with ${\mathcal {A}}$ , and locally isomorphic to ${\mathcal {B}_2}$ . All such locally isomorphic Boundary CFT nets arise in this way. There are only finitely many locally isomorphic Boundary CFT nets and we get them all together. In essence, we show how to directly redefine the C* representation of the restriction of ${\mathcal {B}_2}$ to the half-plane by means of subfactors and local conformal nets of von Neumann algebras on S ¹.     

Finite W-Superalgebras and Truncated Super Yangians

Let ${Y_{m|n}^{\ell}}$ be the super Yangian of general linear Lie superalgebra for ${\mathfrak{gl}_{m|n}}$ . Let ${e \in \mathfrak{gl}_{m\ell|n\ell}}$ be a “rectangular” nilpotent element and ${\mathcal{W}_e}$ be the finite W-superalgebra associated to e. We show that ${Y_{m|n}^{\ell}}$ is isomorphic to ${\mathcal{W}_e}$ .     

Extensions of Ordering Sets of States from Effect Algebras onto Their MacNeille Completions

In (Rie?anová and Zajac in Rep. Math. Phys. 70(2):283–290, 2012) it was shown that an effect algebra E with an ordering set $\mathcal{M}$ of states can by embedded into a Hilbert space effect algebra $\mathcal{E}(l_{2}(\mathcal{M}))$ . We consider the problem when its effect algebraic MacNeille completion $\hat{E}$ can be also embedded into the same Hilbert space effect algebra $\mathcal {E}(l_{2}(\mathcal{M}))$ . That is when the ordering set $\mathcal{M}$ of states on E can be extended to an ordering set of states on $\hat{E}$ . We give an answer for all Archimedean MV-effect algebras and Archimedean atomic lattice effect algebras.     

Joint System Quantum Descriptions Arising from Local Quantumness

We study the entropy flux in the stationary state of a finite one-dimensional sample ${\mathcal{S}}$ connected at its left and right ends to two infinitely extended reservoirs ${\mathcal{R}_{l/r}}$ at distinct (inverse) temperatures ${\beta_{l/r}}$ and chemical potentials ${\mu_{l/r}}$ . The sample is a free lattice Fermi gas confined to a box [0, L] with energy operator ${h_{\mathcal{S}, L}= - \Delta + v}$ . The Landauer-Büttiker formula expresses the steady state entropy flux in the coupled system ${\mathcal{R}_l + \mathcal{S} + \mathcal{R}_r}$ in terms of scattering data. We study the behaviour of this steady state entropy flux in the limit ${L \to \infty}$ and relate persistence of transport to norm bounds on the transfer matrices of the limiting half-line Schrödinger operator ${h_\mathcal{S}}$ .     

Some Properties of Generalized Quantum Operations

Let $\mathcal{B}(\mathcal{H})$ be the set of all bounded linear operators on the separable Hilbert space  $\mathcal{H}$ . A (generalized) quantum operation is a bounded linear operator defined on  $\mathcal{B}(\mathcal{H})$ , which has the form $\varPhi_{\mathcal{A}}(X)=\sum_{i=1}^{\infty}A_{i}XA_{i}^{*}$ , where $A_{i}\in\mathcal{B}(\mathcal{H})$ (i=1,2,…) satisfy $\sum_{i=1}^{\infty}A_{i}A_{i}^{*}\leq \nobreak I$ in the strong operator topology. In this paper, we establish the relationship between the (generalized) quantum operation $\varPhi_{\mathcal{A}}$ and its dual $\varPhi_{\mathcal {A}}^{\dag}$ with respect to the set of fixed points and the noiseless subspace. In particular, we also partially characterize the extreme points of the set of all (generalized) quantum operations and give some equivalent conditions for the correctable quantum channel.     

Large N approach to Kaon decays and mixing 28 years later: \Delta I=1/2 rule, \hat{B}_K,and \Delta M_K

We review and update our results for $K\rightarrow \pi \pi $ decays and $K^0$ – $\bar{K}^0$ mixing obtained by us in the 1980s within an analytic approximate approach based on the dual representation of QCD as a theory of weakly interacting mesons for large $N$ , where $N$ is the number of colors. In our analytic approach the Standard Model dynamics behind the enhancement of $\hbox {Re}A_0$ and suppression of $\hbox {Re}A_2$ , the so-called $\Delta I=1/2$ rule for $K\rightarrow \pi \pi $ decays, has a simple structure: the usual octet enhancement through the long but slow quark–gluon renormalization group evolution down to the scales $\mathcal{O}(1\, {\hbox { GeV}})$ is continued as a short but fast meson evolution down to zero momentum scales at which the factorization of hadronic matrix elements is at work. The inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones and of Wilson coefficients in a momentum scheme improves significantly the matching between quark–gluon and meson evolutions. In particular, the anomalous dimension matrix governing the meson evolution exhibits the structure of the known anomalous dimension matrix in the quark–gluon evolution. While this physical picture did not yet emerge from lattice simulations, the recent results on $\hbox {Re}A_2$ and $\hbox {Re}A_0$ from the RBC-UKQCD collaboration give support for its correctness. In particular, the signs of the two main contractions found numerically by these authors follow uniquely from our analytic approach. Though the current–current operators dominate the $\Delta I=1/2$ rule, working with matching scales $\mathcal{O}(1 \, {\hbox { GeV}})$ we find that the presence of QCD-penguin operator $Q_6$ is required to obtain satisfactory result for $\hbox {Re}A_0$ . At NLO in $1/N$ we obtain $R=\hbox {Re}A_0/\hbox {Re}A_2= 16.0\pm 1.5$ which amounts to an order of magnitude enhancement over the strict large $N$ limit value $\sqrt{2}$ . We also update our results for the parameter $\hat{B}_K$ , finding $\hat{B}_K=0.73\pm 0.02$ . The smallness of $1/N$ corrections to the large $N$ value $\hat{B}_K=3/4$ results within our approach from an approximate cancelation between pseudoscalar and vector meson one-loop contributions. We also summarize the status of $\Delta M_K$ in this approach.     

On the {{\mathcal{N}}=2} Superconformal Index and Eigenfunctions of the Elliptic RS Model

We define an infinite sequence of superconformal indices, ${{\mathcal{I}}_n}$ , generalizing the Schur index for ${{\mathcal{N}}=2}$ theories. For theories of class ${{\mathcal{S}}}$ we then suggest a recursive technique to completely determine ${{\mathcal{I}}_n}$ . The information encoded in the sequence of indices is equivalent to the ${{\mathcal{N}}=2}$ superconformal index depending on a maximal set of fugacities. Mathematically, the procedure suggested in this note provides a perturbative algorithm for computing a set of eigenfunctions of the elliptic Ruijsenaars–Schneider model.     

Charged Higgs boson discovery potential at a 500 GeV e+e− linear collider

The discovery potential for charged Higgs bosons has been studied with full-statistics background simulations for $\sqrt s$ =500 GeV and ?=10fb^?1. For the hadronic decay channels $H^ + H^ - \to \operatorname{c} \bar s\bar cs$ , a microvertex detector is crucial for establishing a signal over the $e^ + e^ - \to t\bar t$ background. A combination with a search in the channels $H^ + H^ - \to c\bar s\tau ^ - \nu ,\tau ^ + \nu \tau ^ - \bar \nu$ allows detection sensitivity for charged Higgs bosons up to a mass of about 210GeV, independent of the charged Higgs decay modes. Sensitivity regions in them _A-tanβ parameter space of the Minimal Supersymmetric extention of the Standard Model (MSSM) are given.     

Higgs revised in supersymmetric economical 3-3-1 model with B/\mu -type terms

We re-investigate the scalar potential and the Higgs sector of the supersymmetric economical 3-3-1 model (SUSYE331) in the presence of the $B/\mu $ -type terms, which has many important consequences. First, the model contains no massless Higgs fields. Second, we prove that the soft mass parameters of the Higgses must be at the $\hbox {SU}(3)_L$ scale. As a result, the masses of the Higgses drift toward this scale except one light real neutral Higgs with the mass of $m_Z|c_{2\gamma }|$ at the tree level. We also show that there are some Higgses containing many properties of the Higgses in the minimal supersymmetric standard model (MSSM), especially in the neutral Higgs sector. One exact relation in the MSSM, $m^2_{H^{\pm }}=m^2_{A}+m^2_W$ , is still true in the SUSYE331. Based on this result we make some comments on the lepton flavor violating decays of these Higgses as one of signatures of new physics in the SUSYE331 model which may be detected by present colliders.     

The Weil Algebra of a Hopf Algebra I: A Noncommutative Framework

We generalize the notion, introduced by Henri Cartan, of an operation of a Lie algebra ${\mathfrak{g}}$ in a graded differential algebra Ω. We define the notion of an operation of a Hopf algebra ${\mathcal{H}}$ in a graded differential algebra Ω which is referred to as a ${\mathcal{H}}$ -operation. We then generalize for such an operation the notion of algebraic connection. Finally we discuss the corresponding noncommutative version of the Weil algebra: The Weil algebra ${W(\mathcal{H})}$ of the Hopf algebra ${\mathcal{H}}$ is the universal initial object of the category of ${\mathcal{H}}$ -operations with connections.     

DKP oscillator in the presence of magnetic field in (1+2)-dimensions for spin-zero and spin-one particles in noncommutative phase space

In view of the discovery of a new boson by the ATLAS and CMS Collaborations at the LHC, we present an update of the global Standard Model (SM) fit to electroweak precision data. Assuming the new particle to be the SM Higgs boson, all fundamental parameters of the SM are known allowing, for the first time, to overconstrain the SM at the electroweak scale and assert its validity. Including the effects of radiative corrections and the experimental and theoretical uncertainties, the global fit exhibits a p-value of 0.07. The mass measurements by ATLAS and CMS agree within 1.3σ with the indirect determination $M_{H}=94^{\,+25}_{\,-22}~\mathrm{GeV}$ . Within the SM the W boson mass and the effective weak mixing angle can be accurately predicted to be M _W =80.359±0.011 GeV and $\sin ^{2}\theta ^{\ell }_{{\rm eff}}= 0.23150\pm 0.00010$ from the global fit. These results are compatible with, and exceed in precision, the direct measurements. For the indirect determination of the top quark mass we find $m_{t}= 175.8^{\:+2.7}_{\:-2.4}~ \mathrm {GeV}$ , in agreement with the kinematic and cross-section-based measurements.     

Mastering the Master Space

Supersymmetric gauge theories have an important but perhaps under-appreciated notion of a master space, which controls the full moduli space. For world-volume theories of D-branes probing a Calabi-Yau singularity ${\mathcal X}$ the situation is particularly illustrative. In the case of one physical brane, the master space ${\mathcal F^b}$ is the space of F-terms and a particular quotient thereof is ${\mathcal X}$ itself. We study various properties of ${\mathcal F^b}$ which encode such physical quantities as Higgsing, BPS spectra, hidden global symmetries, etc. Using the plethystic program we also discuss what happens at higher number N of branes.     

Possible anomalies in Higgs decay: charm-suppression and flavour-violation

It is suggested that the Higgs boson may have a branching ratio into the $c\bar{c}$ mode suppressed by several orders of magnitude compared with conventional predictions and in addition some small but detectable flavour-violating modes such as $b\bar{s}$ and $\tau \bar{\mu}$ . The suggestion is based on a scheme proposed and tested earlier for explaining the mixing pattern and mass hierarchy of fermions in terms of a rotating mass matrix. If confirmed, the effects would cast new light on the geometric origin of fermion generations and of the Higgs field itself.     

Thin-shell wormholes from the regular Hayward black hole

We discuss the formalism of the two Higgs doublet model of type III with CP violation from CP-even CP-odd mixing in the neutral Higgs bosons. The flavor-changing interactions among neutral Higgs bosons and fermions are presented at tree level in this type of model. These assumptions allow the study of rare top decays mediated by a neutral Higgs boson; particularly we are interested in $t\rightarrow c l^+l^-$ . For this process we estimate the upper bounds of the branching ratios $\mathrm{Br }(t\rightarrow c \tau ^+\tau ^-)$ of the order of $10^{-9}\sim 10^{-7}$ for a neutral Higgs boson mass equal to 125 GeV and $\tan \beta =1$ , 1.5, 2, 2.5. For the case of $t\rightarrow c \tau ^+\tau ^-$ the number of possible events is estimated to range from 1 to 10 events, which could be observed in future experiments at LHC with a luminosity of 300  $\hbox {fb}^{-1}$ and 14 TeV for the energy of the center of mass. Also we estimate that the number of events for the process $t\rightarrow c l^+l^-$ in different scenarios is of the order of 2,500.