On Exact Solvability of $\mathcal N$=4 super Yang-Mills

TL;DR

This paper presents a novel ambitwistor framework that encodes solutions of $ =4$ super Yang-Mills equations as real analytic functions on superambitwistor space, enabling a new solution-generating method.

Contribution

It introduces a superambitwistor space approach to exactly solve $ =4$ super Yang-Mills equations through a Riemann-Hilbert-type factorization.

Findings

Solutions are encoded in real analytic functions on superambitwistor space.

A new solution-generating procedure via Riemann-Hilbert factorization.

Framework applies to Minkowski space $ eal^{3,1}$.

Abstract

We consider the ambitwistor description of $\mathcal N$=4 supersymmetric extension of U($N$) Yang-Mills theory on Minkowski space $\mathbb R^{3,1}$. It is shown that solutions of super-Yang-Mills equations are encoded in real analytic U($N$)-valued functions on a domain in superambitwistor space ${\mathcal L}_{\mathbb R}^{5|6}$ of real dimension $(5|6)$. This leads to a procedure for generating solutions of super-Yang-Mills equations on $\mathbb R^{3,1}$ via solving a Riemann-Hilbert-type factorization problem on two-spheres in $\mathcal L_{\mathbb R}^{5|6}$.