2,988 research outputs found
Dimensional Reduction for Conformal Blocks
We consider the dimensional reduction of a CFT, breaking multiplets of the
d-dimensional conformal group SO(d+1,1) up into multiplets of SO(d,1). This
leads to an expansion of d-dimensional conformal blocks in terms of blocks in
d-1 dimensions. In particular, we obtain a formula for 3d conformal blocks as
an infinite sum over 2F1 hypergeometric functions with closed-form
coefficients.Comment: 12 pages, 1 figur
Radial Coordinates for Conformal Blocks
We develop the theory of conformal blocks in CFT_d expressing them as power
series with Gegenbauer polynomial coefficients. Such series have a clear
physical meaning when the conformal block is analyzed in radial quantization:
individual terms describe contributions of descendants of a given spin.
Convergence of these series can be optimized by a judicious choice of the
radial quantization origin. We argue that the best choice is to insert the
operators symmetrically. We analyze in detail the resulting "rho-series" and
show that it converges much more rapidly than for the commonly used variable z.
We discuss how these conformal block representations can be used in the
conformal bootstrap. In particular, we use them to derive analytically some
bootstrap bounds whose existence was previously found numerically.Comment: 27 pages, 9 figures; v2: misprints correcte
The ABC (in any D) of Logarithmic CFT
Logarithmic conformal field theories have a vast range of applications, from
critical percolation to systems with quenched disorder. In this paper we
thoroughly examine the structure of these theories based on their symmetry
properties. Our analysis is model-independent and holds for any spacetime
dimension. Our results include a determination of the general form of
correlation functions and conformal block decompositions, clearing the path for
future bootstrap applications. Several examples are discussed in detail,
including logarithmic generalized free fields, holographic models,
self-avoiding random walks and critical percolation.Comment: 55 pages + appendice
Nanolithography with metastable helium atoms in a high-power standing-wave light field
We have created periodic nanoscale structures in a gold substrate with a
lithography process using metastable triplet helium atoms that damage a
hydrofobic resist layer on top of the substrate. A beam of metastable helium
atoms is transversely cooled and guided through an intense standing-wave light
field. Compared to commonly used low-power optical masks, a high-power light
field (saturation parameter of 10E7) increases the confinement of the atoms in
the standing-wave considerably, and makes the alignment of the experimental
setup less critical. Due to the high internal energy of the metastable helium
atoms (20 eV), a dose of only one atom per resist molecule is required. With an
exposure time of only eight minutes, parallel lines with a separation of 542 nm
and a width of 100 nm (1/11th of the wavelength used for the optical mask) are
created.Comment: 5 pages, 5 figure
Validation of two short dementia screening tests in Indonesia
Validation of two short dementia screening tests in Indonesi
Oophorectomy and hysterectomy may increase dementia risk but only when performed prematurely
Oophorectomy and hysterectomy may increase dementia risk but only when performed prematurel
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