Subleading Color Corrections at Three Loops to the $\operatorname{tr}(\phi^2)$ Three-Point Form Factor in $\mathcal{N} = 4$ Super Yang-Mills Theory

Abstract

We compute three-loop corrections to the three-point form factor of the operator $\operatorname{tr}(\phi^2)$ in $\mathcal{N} = 4$ Super Yang-Mills theory. In particular, our result is valid beyond the leading-color limit and will consequently be an important input towards extending the amplitude-bootstrap program beyond the leading-color approximation. We find that our analytic formulae are strikingly compact expressions in terms of integer linear combinations of generalized polylogarithms of weight six.