EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions

This is a writeup of lectures given at the EPFL Lausanne in the fall of 2012. The topics covered: physical foundations of conformal symmetry, conformal kinematics, radial quantization and the OPE, and a very basic introduction to conformal bootstrap.Comment: 68 pages; v2 - misprints correcte

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

A tauberian theorem for the conformal bootstrap

For expansions in one-dimensional conformal blocks, we provide a rigorous link between the asymptotics of the spectral density of exchanged primaries and the leading singularity in the crossed channel. Our result has a direct application to systems of SL(2,R)-invariant correlators (also known as 1d CFTs). It also puts on solid ground a part of the lightcone bootstrap analysis of the spectrum of operators of high spin and bounded twist in CFTs in d>2. In addition, a similar argument controls the spectral density asymptotics in large N gauge theories.Comment: 36pp; v2: refs and comments added, misprints correcte

Classical Black Hole Production In Quantum Particle Collisions

The semiclassical picture of black hole production in trans-Planckian elementary particle collisions is reviewed.Comment: 5 pages, 7 figures; talk given at the 6th Alexander Friedmann International Seminar on Gravitation and Cosmology, Cargese, France, June 28-July 3, 2004; to appear in the proceedings (Int.J.Mod.Phys.A); v2: typos correcte