Lax pairs of integrable equations in 1 ≤ d ≤ 3 dimensions as reductions of the Lax pair for the self-dual Yang-Mills equations
Symmetry reductions of the self-dual Yang-Mills (SDYM) equations yield various systems of differential equations in lower dimensions. We describe a general scheme of reduction of the Lax pair for the SDYM equations with respect to an arbitrary subgroup of the conformal group. The compatibility of the reduced Lax pair leads to the SDYM equations reduced under the same symmetry group. The scheme is illustrated by three examples.

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

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: 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: 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: Search for resonant diphoton production with the D0 detector.
abstract: We present a search for a narrow resonance in the inclusive diphoton final state using approximately 2.7 fb(-1) of data collected with the D0 detector at the Fermilab Tevatron pp Collider. We observe good agreement between the data and the background prediction, and set the first 95% C.L. upper limits on the production cross section times the branching ratio for decay into a pair of photons for resonance masses between 100 and 150 GeV. This search is also interpreted in the context of several models of electroweak symmetry breaking with a Higgs boson decaying into two photons.

title: Search for charged massive long-lived particles.
abstract: We report on a search for charged massive long-lived particles (CMLLPs), based on 5.2  fb(-1) of integrated luminosity collected with the D0 detector at the Fermilab Tevatron pp collider. We search for events in which one or more particles are reconstructed as muons but have speed and ionization energy loss (dE/dx) inconsistent with muons produced in beam collisions. CMLLPs are predicted in several theories of physics beyond the standard model. We exclude pair-produced long-lived gauginolike charginos below 267 GeV and Higgsino-like charginos below 217 GeV at 95% C.L., as well as long-lived scalar top quarks with mass below 285 GeV.

title: Search for large extra dimensions via single photon plus missing energy final states at sqrt s = 1.96 TeV.
abstract: We report on a search for large extra dimensions in a data sample of approximately 1 fb(-1) of pp[over] collisions at sqrt s=1.96 TeV. We investigate Kaluza-Klein graviton production with a photon and missing transverse energy in the final state. At the 95% C.L. we set limits on the fundamental mass scale M(D) from 884 to 778 GeV for two to eight extra dimensions.

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: A measurement of the $WZ$ and $ZZ$ production cross sections using leptonic final states in 8.6 fb$^{-1}$ of $p\bar{p}$ collisions
abstract: We study the processes p (p) over bar -> WZ -> l(+) vl(+) l(-) and p (p) over bar -> ZZ -> l(+) l(-) v (v) over bar, where l = e or mu. Using 8: 6 fb(-1) of integrated luminosity collected by the D0 experiment at the Fermilab Tevatron collider, we measure the WZ production cross section to be 4.50(-0.66)(+0.63) pb which is consistent with, but slightly larger than, the prediction of the standard model. The ZZ cross section is measured to be 1: 64 +/- 0: 46 pb, in agreement with a prediction of the standard model. Combination with an earlier analysis of the ZZ -> l(+) l(-) l(+) l(-) channel yields a ZZ cross section of 1.44(-0.34)(+0.35) pb.