Level one representations of the simple affine Kac-Moody algebras in their homogeneous gradations
Using the central charge of the Virasoro algebra as a clue, we recall the known constructions of theA, D, E algebras and discuss new Bosonic constructions of the non simply laced affine Kac-Moody algebras: the twistedA, D, E and theB, C, F, andG algebras. These involve interacting Fermions and a generalization of the Frenkel-Kac sign operators which do not form a 2-cocycle when the horizontal algebra has more than one short simple root.

title: Spin-Charge Separation and the Spin Quantum Hall Effect
abstract: We use quantum field theory methods to study the network model for the spin quantum hall transition. When the couplings are fine tuned in a certain way, the spin and charge degrees of freedom, corresponding to the su-percurrent algebras su(2) 0 and osp(2|2) −2 respectively, completely decouple. This simpler theory is exactly solvable and some critical exponents are computed and shown to agree with the recent predictions based on percolation. The general network model is shown to be in a different universality class by identifying the attractive direction of the renormalization group flow.

title: Logarithmic Yangians in WZW Models
abstract: A new action of the Yangians in the WZW models is displayed. Its structure is generic and level-independent. This Yangian is the natural extension at the conformal point of the one unraveled in massive theories with current algebras. Hopefully, this new symmetry of WZW models will lead to a deeper understanding of the integrable structure of conformal field theories and their deformations.

title: On Root Multiplicities of Some Hyperbolic Kac–Moody Algebras
abstract: Using the coset construction, we compute the root multiplicities at level-3 for some hyperbolic Kac–Moody algebras including the basic hyperbolic extension of A11 and E10.

title: Anomalous scaling in the N-point functions of a passive scalar.
abstract: A recent analysis of the 4-point correlation function of the passive scalar advected by a time-decorrelated random flow is extended to the N-point case. It is shown that all stationary-state inertial-range correlations are dominated by homogeneous zero modes of singular operators describing their evolution. We compute analytically the zero modes governing the N-point structure functions and the anomalous dimensions corresponding to them to the linear order in the scaling exponent of the 2-point function of the advecting velocity field. The implications of these calculations for the dissipation correlations are discussed.

title: An Introduction to Yangian Symmetries
abstract: We review some aspects of the quantum Yangians as symmetry algebras of two-dimensional quantum field theories. The plan of these notes is the following: 
 
1 
 
The classical Heisenberg model: 
 
 
 
 
 
 
 
 
 
Non-Abelian symmetries; 
 
 
The generators of the symmetries and the semi-classical Yangians; 
 
 
An alternative presentation of the semi-classical Yangians; 
 
 
Digression on Poisson-Lie groups. 
 
 
Non-Abelian symmetries and the quantum Yangians; 
 
 
The transfer matrix and an alternative presentation of the Yangians; 
 
 
Digression on the double Yangians. 
 
 
 
 
 
2 
 
The quantum Heisenberg chain: 
 
 
 
 
 
 
 
 
 
Non-Abelian symmetries and the quantum Yangians; 
 
 
The transfer matrix and an alternative presentation of the Yangians; 
 
 
Digression on the double Yangians.

title: The BABAR detector: Upgrades, operation and performance
abstract: The BaBar detector operated successfully at the PEP-II asymmetric e +e- collider at the SLAC National Accelerator Laboratory from 1999 to 2008. This report covers upgrades, operation, and performance of the collider and the detector systems, as well as the trigger, online and offline computing, and aspects of event reconstruction since the beginning of data taking.

title: Search for the decay $B^0 \to \gamma \gamma$

title: Measurement of CP asymmetries in $B^0 \to K_s 0 \pi^0 \pi^0$ decays
abstract: We present a preliminary measurement of the time-dependent CP asymmetry for the neutral B-meson decay into the CP = +1 final state KS pi0 pi0, with KS-> pi+ pi- and pi0-> gamma gamma. We use a sample of approximately 227 million B-meson pairs recorded at the Y(4S) resonance by the BaBar detector at the PEP-II B-Factory at SLAC. From a maximum likelihood fit we extract the mixing-induced CP-violation parameter S = 0.84 +/- 0.71(stat} +/- 0.08{syst) and the direct CP-violation parameter C = 0.27 +/- 0.52(stat) +/- 0.13(syst}, where the first uncertainty is statistical and the second systematic.

title: Photon-photon elastic scattering in the visible domain
abstract: We are investigating the direct detection of photon-photon elastic scattering at optical energies. In a first experiment using two high-intensity pulsed laser beams, we have explored the feasibility of the method, and in particular the rejection of back-ground noise. We obtained an upper limit of the photon-photon elastic scattering cross section at 95% confidence level of 10−39 cm2. This limit can be lowered by twenty orders of magnitude by stimulating the scattering by a third beam, and by using high repetition rate existing lasers.

title: Search for a dark photon in e(+)e(-) collisions at BABAR.
abstract: Dark sectors charged under a new Abelian interaction have recently received much attention in the context of dark matter models. These models introduce a light new mediator, the so-called dark photon (A^{'}), connecting the dark sector to the standard model. We present a search for a dark photon in the reaction e^{+}e^{-}→γA^{'}, A^{'}→e^{+}e^{-}, μ^{+}μ^{-} using 514  } of data collected with the BABAR detector. We observe no statistically significant deviations from the standard model predictions, and we set 90% confidence level upper limits on the mixing strength between the photon and dark photon at the level of 10^{-4}-10^{-3} for dark photon masses in the range 0.02-10.2  GeV. We further constrain the range of the parameter space favored by interpretations of the discrepancy between the calculated and measured anomalous magnetic moment of the muon.