56 research outputs found
Recursion Relations for Conformal Blocks
In the context of conformal field theories in general space-time dimension,
we find all the possible singularities of the conformal blocks as functions of
the scaling dimension of the exchanged operator. In particular, we
argue, using representation theory of parabolic Verma modules, that in odd
spacetime dimension the singularities are only simple poles. We discuss how to
use this information to write recursion relations that determine the conformal
blocks. We first recover the recursion relation introduced in 1307.6856 for
conformal blocks of external scalar operators. We then generalize this
recursion relation for the conformal blocks associated to the four point
function of three scalar and one vector operator. Finally we specialize to the
case in which the vector operator is a conserved current.Comment: 55 pages, 12 figures; v2 Typos corrected, conclusions changed,
reference adde
Radial expansion for spinning conformal blocks
This paper develops a method to compute any bosonic conformal block as a
series expansion in the optimal radial coordinate introduced by Hogervorst and
Rychkov. The method reduces to the known result when the external operators are
all the same scalar operator, but it allows to compute conformal blocks for
external operators with spin. Moreover, we explain how to write closed form
recursion relations for the coefficients of the expansions. We study three
examples of four point functions in detail: one vector and three scalars; two
vectors and two scalars; two spin 2 tensors and two scalars. Finally, for the
case of two external vectors, we also provide a more efficient way to generate
the series expansion using the analytic structure of the blocks as a function
of the scaling dimension of the exchanged operator.Comment: 42 pages, 17 figures, 7 Mathematica files, v2: minor changes in the
text, typos correcte
AdS black disk model for small-x DIS
Using the approximate conformal invariance of QCD at high energies we
consider a simple AdS black disk model to describe saturation in DIS. Deep
inside saturation the structure functions have the same power law scaling, F_T
~ F_L ~ 1/x^w, where w is related to the expansion rate of the black disk with
energy. Furthermore, the ratio F_L /F_T is given by the universal value
(1+w)/(3+w), independently of the target. For virtual photon-photon scattering
at high energies we obtain explicit expressions and ratios for the total cross
sections of transverse and longitudinal photons in terms of the single
parameter w.Comment: 5 pages. Minor correction
Bootstrapping the -anomaly in QFTs
We study gapped 4d quantum field theories (QFTs) obtained from a relevant
deformation of a UV conformal field theory (CFT). For simplicity, we assume the
existence of a symmetry and a single -odd stable
particle and no -even particles at low energies. Using unitarity,
crossing and the assumption of maximal analyticity we compute numerically a
lower bound on the value of the -anomaly of the UV CFT as a function of
various non-perturbative parameters describing the two-to-two scattering
amplitude of the particle.Comment: 41 pages + appendices, 20 figure
Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions
We introduce the impact-parameter representation for conformal field theory
correlators of the form A ~ . This representation is
appropriate in the eikonal kinematical regime, and approximates the conformal
partial-wave decomposition in the limit of large spin and dimension of the
exchanged primary. Using recent results on the two-point function < O_1 O_1
>_{shock} in the presence of a shock wave in Anti-de Sitter, and its relation
to the discontinuity of the four-point amplitude A across a kinematical
branch-cut, we find the high spin and dimension conformal partial- wave
decomposition of all tree-level Anti-de Sitter Witten diagrams. We show that,
as in flat space, the eikonal kinematical regime is dominated by the T-channel
exchange of the massless particle with highest spin (graviton dominance). We
also compute the anomalous dimensions of the high-spin O_1 O_2 composites.
Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to
all orders in the gravitational coupling.Comment: JHEP3.cls, 27 pages, 8 figure
Modelling fiber flow in fiberboard manufacturing
Resin weighs substantially on the costs associated with the manufacturing
of MDF (medium-density fiberboard). It is thus important to ensure the
efficiency of resin usage in production lines with the purpose of ensuring
a given internal bond strength (IB) for specific products. Sonae has two
MDF production lines using similar technologies and materials but which
need different resin percentages to reach the same IB. It was asked of the
study group to find out what were the determining factors responsible for
this difference and, if possible, suggest alternatives which will improve resin
efficiency
Coleman meets Schwinger
It is well known that spherical D-branes are nucleated in the presence of an
external RR electric field. Using the description of D-branes as solitons of
the tachyon field on non-BPS D-branes, we show that the brane nucleation
process can be seen as the decay of the tachyon false vacuum. This process can
describe the decay of flux-branes in string theory or the decay of quintessence
potentials arising in flux compactifications.Comment: 5 pages, 2 figure
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