30 research outputs found
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 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 is shown to coincide
with a simpler one, generated by a bilocal scalar field of
dimension (1,1). The modes of V together with the unit operator span an
infinite dimensional Lie algebra 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 ) is proven to be
equivalent to .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 , 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