q-Deformed Supersymmetry and Dynamic Magnon Representations

It was recently noted that the dispersion relation for the magnons of planar N=4 SYM can be identified with the Casimir of a certain deformation of the Poincare algebra, in which the energy and momentum operators are supplemented by a boost generator J. By considering the relationship between J and su(2|2) x R^2, we derive a q-deformed super-Poincare symmetry algebra of the kinematics. Using this, we show that the dynamic magnon representations may be obtained by boosting from a fixed rest-frame representation. We comment on aspects of the coalgebra structure and some implications for the question of boost-covariance of the S-matrix.Comment: 15 pages, LaTeX; (v2) references adde

Path description of type B q-characters

We give a set of sufficient conditions for a Laurent polynomial to be the q-character of a finite-dimensional irreducible representation of a quantum affine group. We use this result to obtain an explicit path description of q-characters for a class of modules in type B. In particular, this proves a conjecture of Kuniba-Ohta-Suzuki.Comment: 32 pages, late

A comment on "Amplification of endpoint structure for new particle mass measurement at the LHC"

We present a comment on the kinematic variable $m_{CT2}$ recently proposed in "Amplification of endpoint structure for new particle mass measurement at the LHC". The variable is designed to be applied to models such as R-parity conserving Supersymmetry (SUSY) when there is pair production of new heavy particles each of which decays to a single massless visible and a massive invisible component. It was proposed in "Amplification of endpoint structure for new particle mass measurement at the LHC" that a measurement of the peak of the $m_{CT2}$ distribution could be used to precisely constrain the masses of the SUSY particles. We show that when Standard Model backgrounds are included in simulations, the sensitivity of the $m_{CT2}$ variable to the SUSY particle masses is more seriously impacted for $m_{CT2}$ than for other previously proposed variables.Comment: 5 page

The optical variability of the narrow line Seyfert 1 galaxy IRAS 13224-3809

We report on a short optical monitoring programme of the narrow-line Seyfert 1 Galaxy IRAS 13224-3809. Previous X-ray observations of this object have shown persistent giant variability. The degree of variability at other wavelengths may then be used to constrain the conditions and emission processes within the nucleus. Optical variability is expected if the electron population responsible for the soft X-ray emission is changing rapidly and Compton-upscattering infrared photons in the nucleus, or if the mechanism responsible for X-ray emission causes all the emission processes to vary together. We find that there is no significant optical variability with a firm upper limit of 2 per cent and conclude that the primary soft X-ray emission region produces little of the observed optical emission. The X-ray and optical emission regions must be physically distinct and any reprocessing of X-rays into the optical waveband occurs some distance from the nucleus. The lack of optical variability indicates that the energy density of infrared radiation in the nucleus is at most equal to that of the ultraviolet radiation since little is upscattered into the optical waveband. The extremely large X-ray variability of IRAS 13224-3809 may be explained by relativistic boosting of more modest variations. Although such boosting enhances X-ray variability over optical variability, this only partially explains the lack of optical variability.Comment: 5 pages with 8 postscript figures. Accepted for publication in MNRA