Speaker: Maximilian Gottwald (HU Berlin)

Title: Hexagons, Gluing & Intersection Theory

Abstract:
The hexagon formalism is an integrability based framework to calculate correlation functions in N=4 Super Yang-Mills theory. The idea is to decompose the correlation function into building blocks called hexagon form factors. In order to correctly reproduce weak-coupling results, the hexagonal patches are dressed with virtual magnons on their non physical edges which is generally referred to as gluing. Consistent methods for an analytic evaluation of such contributions are mostly lacking, even for the simplest non-trivial examples.
However, the recently discovered connection between the Euler integral structure of the gluing processes and intersection theory shows first glimpses of providing the necessary tools for such an analytic calculation. The main goal of this approach is to decompose the Euler integrals into a set of master integrals and solve them by deriving a corresponding system of Pfaffian differential equations.
In this talk the approach will be demonstrated step by step on the one-loop correction to a correlation function of five BPS Operators with length two.