Narrow Results

In the framework of conformal field theory, the mapping from (unbounded) wedge regions of Minkowski spacetime to (bounded) double-cone regions is extended to the Unruh temperature associated to a uniformly accelerated observer. The link between a previous result, the diamond's temperature, and the conformal factor (Weyl rescaling of the metric) is worked out. One thus explains from a mathematical point of view why an observer with finite lifetime experiences the vacuum as a thermal state whatever his acceleration, even vanishing.

Requiring all massless elementary fields to have conformal scaling symmetry removes the conflict between gravitational theory and the quantum theory of elementary particles and fields. Extending this postulate to the scalar field of the Higgs model, dynamical breaking of both gauge and conformal symmetries determines parameters for the interacting fields. In uniform isotropic geometry a modified Friedmann cosmic evolution equation is derived with nonvanishing cosmological constant. Parameters determined by numerical solution are consistent with empirical data for redshifts z ≤ z_* = 1090, including luminosity distances for observed type Ia supernovae and peak structure ratios in the cosmic microwave background (CMB). The theory does not require dark matter.

Recent cosmological observations and compatible theory offer an understanding of long-mysterious dark matter and dark energy. The postulate of universal conformal local Weyl scaling symmetry, without dark matter, modifies action integrals for both Einstein–Hilbert gravitation and the Higgs scalar field by gravitational terms. Conformal theory accounts for both observed excessive external galactic orbital velocities and for accelerating cosmic expansion. SU(2) symmetry-breaking is retained by the conformal scalar field, which does not produce a massive Higgs boson, requiring an alternative explanation of the observed LHC 125 GeV resonance. Conformal theory is shown here to be compatible with a massive neutral particle or resonance $W_2$ at 125 GeV, described as binary scalars $g_{\mu \nu }{W}_{-}^{\mu }{W}_{+}^{\nu }$ and $g_{\mu \nu }{Z}^{\mu \ast }{Z}^{\nu }$ interacting strongly via quark exchange. Decay modes would be consistent with those observed at LHC. Massless scalar field $\mathrm{\Phi }$ is dressed by the $W_2$ field to produce Higgs Lagrangian term $\lambda {({\mathrm{\Phi }}^{†}\mathrm{\Phi })}^2$ with the empirical value of $\lambda$ known from astrophysics.

We study the production of the vector U-unparticle stuff and a single photon in decays of a dilaton. The signals of an unparticle can be detected through the missing energy and momentum distribution carried away by U once it was produced in radiative decay of a dilaton. The continuous energy spectrum of the emitted photons encoding the recoil unparticle can be measured in precision studies of rare decays of the dilaton or Higgs-boson after their discoveries.

This paper studies the Yang–Lee edge singularity of 2-dimensional (2D) Ising model through a quantum spin chain. In particular, finite-size scaling measurements on the quantum spin chain are used to determine the low-lying excitation spectrum and central charge at the Yang–Lee edge singularity. The measured values are consistent with predictions for the (A₄, A₁) minimal conformal field theory.

We review the definition by Perlick of standard clocks in a Weyl geometry and show how a congruence of clocks can be used to fix the conformal gauge in the EPS framework. Examples are discussed in detail.

We work on a class of non-stationary vacuum space-times admitting a conformal compactification that is smooth at null and timelike infinity. Via a conformal transformation, the existence of a scattering operator for field equations is interpreted as the well-posedness of a Goursat problem on null infinity. We solve the Goursat problem in the case of Dirac and Maxwell fields. The case of the wave equation is also discussed and it is shown why the method cannot be applied at present. Then the conformal scattering operator is proved to be equivalent to an analytical scattering operator defined in terms of classical wave operators.

With a substantial amount of simulations, we have explored the system across a wide range of lattice scales. We have located a lattice artifact, first order bulk transition, have studied its properties, and found that the flavor-singlet scalar meson mass vanishes at the critical endpoint. We will discuss the lattice phase diagrams and the continuum limits for both a S_χSB phase and an IR conformal phase, and compare results with other groups.