Ultraviolet Behavior of N=8 Supergravity

TL;DR

This paper discusses the surprising ultraviolet properties of N=8 supergravity, showing it behaves as well as N=4 super-Yang-Mills theory up to four loops, and explains the computational methods used to analyze these amplitudes.

Contribution

It introduces the ultraviolet behavior of N=8 supergravity and details the computational tools like KLT relations and unitarity method used for multi-loop amplitude evaluation.

Findings

N=8 supergravity is no worse than N=4 super-Yang-Mills theory up to four loops.

The paper explains how to extract ultraviolet divergences from multi-loop amplitudes.

Computational tools such as KLT relations and unitarity method are essential for these analyses.

Abstract

In these lectures I describe the remarkable ultraviolet behavior of N=8 supergravity, which through four loops is no worse than that of N=4 super-Yang-Mills theory (a finite theory). I also explain the computational tools that allow multi-loop amplitudes to be evaluated in this theory - the KLT relations and the unitarity method - and sketch how ultraviolet divergences are extracted from the amplitudes.