Generating-function method for tensor products

This is the first of two articles devoted to a exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit of fusions rules. We start by reviewing Sharp's character method. An alternative approach to the construction of tensor-product generating functions is then presented which overcomes most of the technical difficulties associated with the character method. It is based on the reformulation of the problem of calculating tensor products in terms of the solution of a set of linear and homogeneous Diophantine equations whose elementary solutions represent ``elementary couplings''. Grobner bases provide a tool for generating the complete set of relations between elementary couplings and, most importantly, as an algorithm for specifying a complete, compatible set of ``forbidden couplings''.Comment: Harvmac (b mode : 39 p) and Pictex; this is a substantially reduced version of hep-th/9811113 (with new title); to appear in J. Math. Phy

Generating-function method for fusion rules

This is the second of two articles devoted to an exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper focuses on fusion rules, using the machinery developed for tensor products in the companion article. Although the Kac-Walton algorithm provides a method for constructing a fusion generating function from the corresponding tensor-product generating function, we describe a more powerful approach which starts by first defining the set of fusion elementary couplings from a natural extension of the set of tensor-product elementary couplings. A set of inequalities involving the level are derived from this set using Farkas' lemma. These inequalities, taken in conjunction with the inequalities defining the tensor products, define what we call the fusion basis. Given this basis, the machinery of our previous paper may be applied to construct the fusion generating function. New generating functions for sp(4) and su(4), together with a closed form expression for their threshold levels are presented.Comment: Harvmac (b mode : 47 p) and Pictex; to appear in J. Math. Phy

The optical companion to the binary millisecond pulsar J1824-2452H in the globular cluster M28

We report on the optical identification of the companion star to the eclipsing millisecond pulsar PSR J1824-2452H in the galactic globular cluster M28 (NGC 6626). This star is at only 0.2" from the nominal position of the pulsar and it shows optical variability (~ 0.25 mag) that nicely correlates with the pulsar orbital period. It is located on the blue side of the cluster main sequence, ~1.5 mag fainter than the turn-off point. The observed light curve shows two distinct and asymmetric minima, suggesting that the companion star is suffering tidal distortion from the pulsar. This discovery increases the number of non-degenerate MSP companions optically identified so far in globular clusters (4 out of 7), suggesting that these systems could be a common outcome of the pulsar recycling process, at least in dense environments where they can be originated by exchange interactions.Comment: accepted for publication on ApJ, 17 pages, 5 figure

Constraining the luminosity function parameters and population size of radio pulsars in globular clusters

Studies of the Galactic population of radio pulsars have shown that their luminosity distribution appears to be log-normal in form. We investigate some of the consequences that occur when one applies this functional form to populations of pulsars in globular clusters. We use Bayesian methods to explore constraints on the mean and standard deviation of the luminosity function, as well as the total number of pulsars, given an observed sample of pulsars down to some limiting flux density, accounting for measurements of flux densities of individual pulsars as well as diffuse emission from the direction of the cluster. We apply our analysis to Terzan 5, 47 Tucanae and M 28, and demonstrate, under reasonable assumptions, that the number of potentially observable pulsars should be within 95% credible intervals of $147^{+112}_{-65}$, $83^{+54}_{-35}$ and $100^{+91}_{-52}$, respectively. Beaming considerations would increase the true population size by approximately a factor of two. Using non-informative priors, however, the constraints are not tight due to the paucity and quality of flux density measurements. Future cluster pulsar discoveries and improved flux density measurements would allow this method to be used to more accurately constrain the luminosity function, and to compare the luminosity function between different clusters.Comment: 9 pages, 4 figures, Accepted for publication in MNRA

Berenstein-Zelevinsky triangles, elementary couplings and fusion rules

We present a general scheme for describing su(N)_k fusion rules in terms of elementary couplings, using Berenstein-Zelevinsky triangles. A fusion coupling is characterized by its corresponding tensor product coupling (i.e. its Berenstein-Zelevinsky triangle) and the threshold level at which it first appears. We show that a closed expression for this threshold level is encoded in the Berenstein-Zelevinsky triangle and an explicit method to calculate it is presented. In this way a complete solution of su(4)_k fusion rules is obtained.Comment: 14 page

Extended radio emission in the galaxy cluster MS 0735.6+7421 detected with the Karl G. Jansky Very Large Array

MS 0735.6+7421 ($z = 0.216$) is a massive cool core galaxy cluster hosting one of the most powerful active galactic nuclei (AGN) outbursts known. The radio jets of the AGN have carved out an unusually large pair of X-ray cavities, each reaching a diameter of $200$ kpc. This makes MS 0735.6+7421 a unique case to investigate active galactic nuclei feedback processes, as well as other cluster astrophysics at radio wavelengths. We present new low-radio-frequency observations of MS 0735.6+7421 taken with the Karl G. Jansky Very Large Array (VLA): 5 hours of P-band ($224-480$ MHz) and 5 hours of L-band ($1-2$ GHz) observations, both in C configuration. Our VLA P-band ($224-480$ MHz) observations reveal the presence of a new diffuse radio component reaching a scale of $\sim$ $900$ kpc in the direction of the jets and of $\sim$ $500$ kpc in the direction perpendicular to the jets. This component is centered on the cluster core and has a radio power scaled at $1.4$ GHz of $P_{1.4\text{ GHz}} = (4\pm2)\times 10^{24}$ WHz$^{-1}$. Its properties are consistent with those expected from a radio mini-halo as seen in other massive cool core clusters, although it may also be associated with radio plasma that has diffused out of the X-ray cavities. Observations at higher spatial resolution are needed to fully characterize the properties and nature of this component. We also suggest that if radio mini-halos originate from jetted activity, we may be witnessing the early stages of this process.Comment: 11 pages, 7 figures, submitted to MNRA