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