Heterotic compactifications on nearly Kähler manifolds
We consider compactifications of heterotic supergravity on anti-de Sitter space, with a six-dimensional nearly Kähler manifold as the internal space. Completing the model proposed by Frey and Lippert  with the particular choice of SU(3)/U(1) × U(1) for the internal manifold, we show that it satisfies not only the supersymmetry constraints but also the equations of motion with string corrections of order α′. Furthermore, we present a nonsupersymmetric model. In both solutions we find confirmed a recent result of Ivanov [18] on the connection used for anomaly cancellation. Interestingly, the volume of the internal space is fixed by the supersymmetry constraints and/or the equations of motion.

title: Fundamental chiral strings
abstract: The problem of the non-uniqueness of the string theory in the space Rd-1,1 with d ≤ 10 and the procedure of the compactification and the deompactification are discussed. We consider a compact bosonic string defined as a closed string moving in the Lorentizian torus T25,1 and introduce fundamental chiral bosonic string (FCBS) as a universal cover of a compact string. It is shown that the Fock spaces of any standard strings are embedded into the Fock space of FCBS.

title: On nonperturbative solutions of superstring field theory
abstract: Nonperturbative solutions to the nonlinear field equations in the NS sector of cubic as well as nonpolynomial superstring field theory can be obtained from a linear equation which includes a “spectral” parameter λ and a coboundary operator Q ( λ ). We borrow a simple ansatz from the dressing method (for generating solitons in integrable field theories) and show that classical superstring fields can be constructed from any string field  T subject merely to Q ( λ ) T =0. Following the decay of the non-BPS D9 brane in IIA theory and shifting the background to the tachyon vacuum, we repeat the arguments in vacuum superstring field theory and outline how to compute classical solutions explicitly.

title: Solving string field equations: new uses for old tools
abstract: It is argued that the (NS-sector) superstring field equations are integrable, i.e. their solutions are obtainable from linear equations. We adapt the 25-year-old solution-generating “dressing” method and reduce the construction of nonperturbative superstring configurations to a specific cohomology problem. The application to vacuum superstring field theory is outlined.

title: Noncommutative instantons in higher dimensions, vortices and topological K-cycles
abstract: We construct explicit BPS and non-BPS solutions of the U(2k) Yang-Mills equations on the noncommutative space 2nθ × S2 with finite energy and topological charge. By twisting with a Dirac multi-monopole bundle over S2, we reduce the Donaldson-Uhlenbeck-Yau equations on 2nθ × S2 to vortex-type equations for a pair of U(k) gauge fields and a bi-fundamental scalar field on 2nθ. In the SO(3)-invariant case the vortices on 2nθ determine multi-instantons on 2nθ × S2. We show that these solutions give natural physical realizations of Bott periodicity and vector bundle modification in topological K-homology, and can be interpreted as a blowing-up of D0-branes on 2nθ into spherical D2-branes on 2nθ × S2. In the generic case with broken rotational symmetry, we argue that the D0-brane charges on 2nθ × S2 provide a physical interpretation of the Adams operations in K-theory.

title: Solutions of Yang-Mills and Yang-Mills-Higgs equations

title: Searches for new physics at Tevatron: Most recent results
abstract: The most recent results obtained from searches of particles and phenomena beyond the Standard Model (new physics) in the D0 and CDF experiments at the Tevatron accelerator (FNAL, USA) on the basis of statistics corresponding to the integrated luminosity of up to 4 fb−1 in 2009 are considered. Particular attention is given to the most recent results on searches for a supersymmetric Higgs boson.

title: Search for pair production of the scalar top quark in muon+tau final states
abstract: We present a search for the pair production of scalar top quarks ($\tilde{t}_{1}$), the lightest supersymmetric partners of the top quarks, in $p\bar{p}$ collisions at a center-of-mass energy of 1.96 TeV, using data corresponding to an integrated luminosity of {7.3 $fb^{-1}$} collected with the \dzero experiment at the Fermilab Tevatron Collider. Each scalar top quark is assumed to decay into a $b$ quark, a charged lepton, and a scalar neutrino ($\tilde{\nu}$). We investigate final states arising from $\tilde{t}_{1} \bar{\tilde{t}_{1}} \rightarrow b\bar{b}\mu\tau \tilde{\nu} \tilde{\nu}$ and $\tilde{t}_{1} \bar{\tilde{t}_{1}} \rightarrow b\bar{b}\tau\tau \tilde{\nu} \tilde{\nu}$. With no significant excess of events observed above the background expected from the standard model, we set exclusion limits on this production process in the ($m_{\tilde{t}_{1}}$,$m_{\tilde{\nu}}$) plane.

title: Combination of CDF and D0 measurements of the W boson helicity in top quark decays
abstract: We report the combination of recent measurements of the helicity of the W boson from top quark decay by the CDF and D0 collaborations, based on data samples corresponding to integrated luminosities of 2.7-5.4 fb(-1) of p (p) over bar collisions collected during Run II of the Fermilab Tevatron collider. Combining measurements that simultaneously determine the fractions of W bosons with longitudinal (f(0)) and right-handed (f(+)) helicities, we find f(0) = 0.722 +/- 0.081[+/- 0.062(stat) +/- 0.052(syst)] and f(+) = -0.033 +/- 0.046[+/- 0.034(stat) +/- 0.031(syst)]. Combining measurements where one of the helicity fractions is fixed to the value expected in the standard model, we find f(0) = 0.682 +/- 0.057[+/- 0.035(stat) +/- 0.046(syst)] for fixed f(+) and f(+) = -0.015 +/- 0.035[+/- 0.018(stat) +/- 0.030(syst)] for fixed f(0). The results are consistent with standard model expectations.

title: Recent Results from Brookhaven E852 Experiment
abstract: Experiment E852 at Brookhaven National Laboratory is an experiment in meson spectroscopy configured to detect both neutral and charged final states of π−p collisions at 18 GeV/c. The main goal of this experiment is to search for the signs of mesons which cannot be described in the scope of the constituent quark model, with an emphasis on the meson with the manifestly exotic quantum numbers. In this talk the description of the experimental apparatus along with a general overview of the latest E852 results are presented.

title: Observation and properties of the orbitally excited B_(s2)(*) meson.
abstract: We report the direct observation of the excited L=1 state B_(s2)(*) in fully reconstructed decays to B+K-. The mass of the B_(s2)(*) meson is measured to be 5839.6+/-1.1(stat)+/-0.7(syst) MeV/c(2), and its production rate relative to the B+ meson is measured to be [1.15+/-0.23(stat)+/-0.13(syst)]%.