Conformal Transformations and the SLE Partition
Function Martingale

We present an implementation in conformal field theory (CFT) of local
finite conformal transformations fixing a point. We give explicit constructions when
the fixed point is either the origin or the point at infinity. Both cases involve the
exponentiation of a Borel subalgebra of the Virasoro algebra. We use this to build
coherent state representations and to derive a close analog of Wick’s theorem for the
Virasoro algebra. This allows to compute the conformal partition function in non
trivial geometries obtained by removal of hulls from the upper half-plane. This is
then applied to stochastic Loewner evolutions (SLE). We give a rigorous derivation
of the equations, obtained previously by the authors, that connect the stochastic
Loewner equation to the representation theory of the Virasoro algebra. We give a
new proof that this construction enumerates all polynomial SLE martingales. When
one of the hulls removed from the upper half-plane is the SLE hull, we show that
the partition function reduces to a useful local martingale known to probabilists,
thereby unraveling its CFT origin.

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: 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: 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: 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: The laser wakefield acceleration experiment at Ecole Polytechnique
abstract: A laser wakefield electron acceleration experiment has been set-up at Ecole Polytechnique. An electron beam with 3 MeV total energy is injected in a plasma wave generated by laser wakefield using the new LULI CPA laser (400 fs [FWHM], I 17  W/cm 2 ). The first results show an effective acceleration of the order of 1 MeV, with a maximum when the electron density is close to the optimum value for which the laser pulse length is about half the plasma wavelength.

title: On triple focusing dipole magnets
abstract: We present a general, paraxial study of triple focusing (i.e., stigmatic and non-dispersive) index-free dipole magnets. The transcendental equations which describe such magnets lead to a second-degree polynomial equation which we solve analytically. The two solutions of this equation correspond to magnets having either one or no intermediate focal points in the vertical direction. The first-order optical properties of the physical solutions are studied.

title: Constraints on r($B$) and $\gamma$ in $B^\pm \to D^{(*)} 0 K^\pm$ decays by a Dalitz analysis of $D^0 \to K_{S} \pi^{-} \pi^{+}$

title: The plasma beat-wave acceleration experiment at Ecole Polytechnique
abstract: We present an experiment for demonstrating the principle of plasma beat-wave acceleration. The beating of two Nd-laser pulses creates a relativistic plasma wave in a deuterium plasma. Electrons at an energy of 3 MeV are injected into the plasma. We observe several hundred electrons accelerated up to 3.7 MeV. This paper is mainly devoted to the description of the experimental apparatus. In the design of the apparatus, we gave particular attention to efficient electron injection and to background noise suppression. We present also some preliminary results of electron acceleration experiments.

title: Search for low-mass dark-sector Higgs bosons.
abstract: Recent astrophysical and terrestrial experiments have motivated the proposal of a dark sector with GeV-scale gauge boson force carriers and new Higgs bosons. We present a search for a dark Higgs boson using 516 fb(-1) of data collected with the BABAR detector. We do not observe a significant signal and we set 90% confidence level upper limits on the product of the standard model-dark-sector mixing angle and the dark-sector coupling constant.