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

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 ${\mathcal{L}}_{\mathbb{R}}^{5|6}$.

arXiv comment23 pages, v2: clarifying comments added, published version

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• Ambitwistor Yang-Mills Theory Revisited