Conformal field theories with infinitely many conservation laws

Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [BNRT]. Recently, conformal field theories "with higher spin symmetry" were considered for D=3 in [MZ] where a similar result was obtained (exploiting earlier study of CFT correlators). We suggest that the proper generalization of the notion of a 2D chiral algebra to arbitrary (even or odd) dimension is precisely a CFT with an infinite series of conserved currents. We shall recast and complement (part of) the argument of Maldacena and Zhiboedov into the framework of our earlier work. We extend to D=4 the auxiliary Weyl-spinor formalism developed in [GPY] for D=3. The free field construction only follows for D>3 under additional assumptions about the operator product algebra. In particular, the problem of whether a rational CFT in 4D Minkowski space is necessarily trivial remains open.Comment: 24 pages, Lecture at the TH Journal Club (CERN, February 2012

Four Dimensional CFT Models with Rational Correlation Functions

Recently established rationality of correlation functions in a globally conformal invariant quantum field theory satisfying Wightman axioms is used to construct a family of soluble models in 4-dimensional Minkowski space-time. We consider in detail a model of a neutral scalar field $\phi$ of dimension 2. It depends on a positive real parameter c, an analogue of the Virasoro central charge, and admits for all (finite) c an infinite number of conserved symmetric tensor currents. The operator product algebra of $\phi$ is shown to coincide with a simpler one, generated by a bilocal scalar field $V(x_1,x_2)$ of dimension (1,1). The modes of V together with the unit operator span an infinite dimensional Lie algebra $L_V$ whose vacuum (i.e. zero energy lowest weight) representations only depend on the central charge c. Wightman positivity (i.e. unitarity of the representations of $L_V$) is proven to be equivalent to $c \in N$.Comment: 28 pages, LATEX, amsfonts, latexsym. Proposition 2.3, and Conjecture in Sec. 6 are revised. Minor errors are correcte

Grand Unification Signal from Ultra High Energy Cosmic Rays?

The spectrum of ultrahigh energy (above \approx 10^{9} GeV) cosmic rays is consistent with the decay of GUT scale particles. The predicted mass is m_X=10^b GeV, where b=14.6_{-1.7}^{+1.6}.Comment: 4 pages, 3 figures one figure removed, one table added, conclusions essentially remained the same within errorbar

Ultrahigh energy cosmic rays from collisional annihilation revisited

We re-examine collisional annihilation of superheavy dark matter particles in dark matter density spikes in the galactic halo as a possible source of ultrahigh energy cosmic rays. We estimate the possible flux in a way that does not depend on detailed assumptions about the density profiles of dark matter clumps. The result confirms that collisional annihilation is compatible with annihilation cross sections below the unitarity bounds for superheavy dark matter if the particles can form dense cores in dark matter substructure, and it provides estimates for core sizes and densities. The ensuing clumpy source distribution in the galactic halo will be tested within a few years of operation of the Pierre Auger observatory.Comment: 9 pages, new section included, introduction shortened, to appear in Can. J. Phy

Comparison of Atmospheric Neutrino Flux Calculations at Low Energies

We compare several different calculations of the atmospheric neutrino flux in the energy range relevant for contained neutrino interactions, and we identify the major sources of difference among the calculations. We find nothing that would affect the predicted ratio of $\nu_e/\nu_\mu$, which is nearly the same in all calculations. Significant differences in normalization arise primarily from different treatment of pion production by interactions of protons in the atmosphere. Different assumptions about the primary spectrum and treatment of the geomagnetic field are also of some importance.Comment: 15 pages, RevTeX , 5 postscript figures, submitted to Phys. Rev.

The Magnetized Universe

Cosmology, high-energy physics and astrophysics are converging on the study of large-scale magnetic fields. While the experimental evidence for the existence of large-scale magnetization in galaxies, clusters and superclusters is rather compelling, the origin of the phenomenon remains puzzling especially in light of the most recent observations. The purpose of the present review is to describe the physical motivations and some of the open theoretical problems related to the existence of large-scale magnetic fields.Comment: 147 pages, 10 included figures. Few corrected typos and added reference