704 research outputs found
Central Charge Bounds in 4D Conformal Field Theory
We derive model-independent lower bounds on the stress tensor central charge
C_T in terms of the operator content of a 4-dimensional Conformal Field Theory.
More precisely, C_T is bounded from below by a universal function of the
dimensions of the lowest and second-lowest scalars present in the CFT. The
method uses the crossing symmetry constraint of the 4-point function, analyzed
by means of the conformal block decomposition.Comment: 16 pages, 6 figure
OPE Convergence in Conformal Field Theory
We clarify questions related to the convergence of the OPE and conformal
block decomposition in unitary Conformal Field Theories (for any number of
spacetime dimensions). In particular, we explain why these expansions are
convergent in a finite region. We also show that the convergence is
exponentially fast, in the sense that the operators of dimension above Delta
contribute to correlation functions at most exp(-a Delta). Here the constant
a>0 depends on the positions of operator insertions and we compute it
explicitly.Comment: 26 pages, 6 figures; v2: a clarifying note and two refs added; v3:
note added concerning an extra constant factor in the main error estimate,
misprint correcte
Partly Supersymmetric Grand Unification
It is shown how grand unification can occur in models which are partly
supersymmetric. The particle states which are composite do not contribute to
the running of gauge couplings above the compositeness scale, while the
elementary states contribute the usual large logarithmns. This introduces a new
differential running contribution to the gauge couplings from partly composite
SU(5) matter multiplets. In particular, for partly supersymmetric models, the
incomplete SU(5) elementary matter multiplets restore gauge coupling
unification even though the usual elementary gaugino and Higgsino contributions
need not be present.Comment: 14 pages, LaTe
The Three Dimensional Dual of 4D Chirality
Chiral gauge theories can be defined in four-dimensional Anti de Sitter
space, but AdS boundary conditions explicitly break the chiral symmetry in a
specific, well defined manner, which in turns results in an anomalous Ward
identity. When the 4D theory admits a dual description in terms of a 3D CFT,
the 3D dual of the broken chiral symmetry is a certain double-trace deformation
of the CFT, which produces the same anomalous chiral Ward identities that
obtains in the 4D bulk theory.Comment: 10 pages, small misprints corrected, reference [16] updated. Version
to appear in JHE
More Holography from Conformal Field Theory
We extend the work of [4] to support the conjecture that any conformal field
theory with a large N expansion and a large gap in the spectrum of anomalous
dimensions has a local bulk dual. We count to O(1/N^2) the solutions to the
crossing constraints in conformal field theory for a completely general scalar
four-point function and show that, to this order, the counting matches the
number of independent interactions in a general scalar theory on Anti-de Sitter
space. We introduce parity odd conformal blocks for this purpose.Comment: 19 page
Dirac Neutrino Masses with Planck Scale Lepton Number Violation
It is shown how pure Dirac neutrino masses can naturally occur at low
energies even in the presence of Planck scale lepton number violation. The
geometrical picture in five dimensions assumes that the lepton number symmetry
is explicitly broken on the Planck brane while the right-handed neutrino is
localised on the TeV brane. This physical separation in the bulk causes the
global lepton number to be preserved at low energies. A small wavefunction
overlap between the left-handed and right-handed neutrinos then naturally leads
to a small Dirac Yukawa coupling. By the AdS/CFT correspondence there exists a
purely four-dimensional dual description in which the right-handed neutrino is
a composite CFT bound state. The global lepton number is violated at the Planck
scale in a fundamental sector whose mixing into the composite sector is highly
suppressed by CFT operators with large anomalous dimensions. A similar small
mixing is then also responsible for generating a naturally small Dirac Yukawa
coupling between the fundamental left-handed neutrino and the composite
right-handed neutrino.Comment: 12 pages, LaTeX; v2: references added; v3: another reference adde
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