Vertex operator algebras of rank 2 - the Mathur-Mukhi-Sen theorem revisited

Let $V$ be a strongly regular vertex operator algebra and let $\frak{ch}_V$ be the space spanned by the characters of the irreducible $V$-modules.\ It is known that $\frak{ch}_V$ is the space of solutions of a so-called \emph{modular linear differential equation (MLDE)}.\ In this paper we obtain a near-classification of those $V$ for which the corresponding MLDE is irreducible and monic of order $2$.\ As a consequence we derive the complete classification when $V$ has exactly two simple modules.\ It turns out that $V$ is either one of four affine Kac-Moody algebras of level $1$, or the Yang-Lee Virasoro model of central charge ${-}22/5$.\ Our proof establishes new connections between the characters of $V$ and Gauss hypergeometric series, and puts the finishing touches to work of Mathur, Mukhi and Sen who first considered this problem forty years ago

Study of fast electron generation using multi beam of LFEX-class laser

Fast Ignition Realization Experiment project phase-I (FIREX-I) is being performed at Institute of Laser Engineering, Osaka University. In this project, the four-beam bundled high-energy Petawatt laser (LFEX) is being operated. LFEX laser provides great multi-beam irradiation flexibility, with the possibility of arrange the pulses in temporal sequence, spatially separate them in distinct spots of focus them in a single spot. In this paper, we study the two-beam interference effects on high-intensity picosecond laser-plasma interaction (LPI) by two-dimensional relativistic Particle-In-Cell simulations. The interference causes surface perturbation, which enhances laser absorption and underdense plasma generation, increasing the accelerated electron number and their slope temperature. The laser-to-electron energy conversion efficiency for two-beam interference case is suitable for Fast Ignition (FI) compared to the single beam case, but the increment of fast electron divergence leads to lower energy coupling. To optimize the target design for FI, these interference effects should be taken into consideration

The tensor structure on the representation category of the Wp\mathcal{W}_p triplet algebra

We study the braided monoidal structure that the fusion product induces on the abelian category $\mathcal{W}_p$-mod, the category of representations of the triplet $W$-algebra $\mathcal{W}_p$. The $\mathcal{W}_p$-algebras are a family of vertex operator algebras that form the simplest known examples of symmetry algebras of logarithmic conformal field theories. We formalise the methods for computing fusion products, developed by Nahm, Gaberdiel and Kausch, that are widely used in the physics literature and illustrate a systematic approach to calculating fusion products in non-semi-simple representation categories. We apply these methods to the braided monoidal structure of $\mathcal{W}_p$-mod, previously constructed by Huang, Lepowsky and Zhang, to prove that this braided monoidal structure is rigid. The rigidity of $\mathcal{W}_p$-mod allows us to prove explicit formulae for the fusion product on the set of all simple and all projective $\mathcal{W}_p$-modules, which were first conjectured by Fuchs, Hwang, Semikhatov and Tipunin; and Gaberdiel and Runkel.Comment: 58 pages; edit: added references and revisions according to referee reports. Version to appear on J. Phys.

Test of the Conserved Vector Current Hypothesis by beta-ray Angular Distribution Measurement in the Mass-8 System

The beta-ray angular correlations for the spin alignments of 8Li and 8B have been observed in order to test the conserved vector current (CVC) hypothesis. The alignment correlation terms were combined with the known beta-alpha-angular correlation terms to determine all the matrix elements contributing to the correlation terms. The weak magnetism term, 7.5\pm0.2, deduced from the beta-ray correlation terms was consistent with the CVC prediction 7.3\pm0.2, deduced from the analog-gamma-decay measurement based on the CVC hypothesis. However, there was no consistent CVC prediction for the second-forbidden term associated with the weak vector current. The experimental value for the second-forbidden term was 1.0 \pm 0.3, while the CVC prediction was 0.1 \pm 0.4 or 2.1 \pm 0.5.Comment: 31 pages, 12 figures, Accepted for publication in Phys. Rev.