2019

The Schroedinger Visiting Professor in 2019 is Prof. Lance J. Dixon (Stanford University, SLAC National Accelerator Laboratory).

Host: Prof. Thomas Gehrmann (UZH), Prof. Charalampos Anastasiou (ETH Zurich)

Dates of visit: May 19 - June 25, 2019

Schroedinger Lecture 2019

DownloadPoster (PDF, 181 KB)

Title: Particle Scattering and Number Theory

Date: Monday, May 27, 2019

Time: 14.15 h
(followed by an apéro in the DownloadFood Market (PDF, 295 KB), building HPR)

Location: ETH Hönggerberg, HPH G 3

Abstract: From the softest of interactions of a magnetic field with an electron, to the most violent collisions at the Large Hadron Collider, precision quantum field theory produces numbers and functions with interesting number-theoretic properties. In many examples a co-action principle holds, an invariance under a "cosmic" Galois group. I will provide several arenas in which this principle can be seen at work, including perhaps the richest set of theoretical data, scattering amplitudes in planar N=4 super-Yang-Mills theory.

Short courses on "The Hexagon Function Bootstrap for Planar N=4 Super-Yang-Mills Theory"

Dates: Monday, June 3, 2019
Wednesday, June 5, 2019
Friday, June 7, 2019

Location: ETH Hönggerberg, HIT E 41.1

Each course starts at 10.30 h.

Abstract: In the planar limit of a large number of colors, N=4 super Yang-Mills theory is integrable, and remarkable advances have been made in determining operator anomalous dimensions and more to all loop orders. In this series of lectures I'll describe recent progress in constructing scattering amplitudes in this theory to high loop order. Planar N=4 amplitudes are dual to light-like polygonal Wilson-loops, and are only nontrivial for six or more gluons. The spaces of multi-variable functions to which the amplitudes belong are so restrictive that in some cases only a few constraints are needed to simply "write down the answer". This can be done through seven loops in the six-gluon case, and (at "symbol" level) through four loops in the seven-gluon case. The lecture series will describe how to construct the polylogarithmic hexagon functions for the six-point case, including imposing constraints from branch cuts and (extended) Steinmann relations. I'll show how to use a "coproduct" formalism to describe the functions and to take various limits of them in order to impose constraints and verify the correct limiting behavior. I'll also discuss aspects of the co-action principle in more detail, the need to normalize the amplitudes properly, and the high loop order behavior in comparison with semi-classical results that are available at strong coupling via the AdS/CFT correspondence.