The massless hexagon integral in D = 6 dimensions

TL;DR

The paper computes the finite massless one-loop hexagon integral in six dimensions by exploiting dual conformal invariance and a Mellin-Barnes representation, then simplifies the result to a compact weight-3 expression in terms of polylogarithms using a symbol-map approach. The final dual-conformally invariant formula depends on three cross ratios $u_1,u_2,u_3$ and is expressed via $x_i^{\pm}$, $\Delta$, and the symbol-correcting parameter $\chi$. The authors observe a close structural similarity to the remainder function of the two-loop hexagon Wilson loop in four dimensions, suggesting that $I_6^{D=6}$ could serve as a computational probe for higher-loop amplitudes and Wilson loops.

Abstract

We evaluate the massless one-loop hexagon integral in six dimensions. The result is given in terms of standard polylogarithms of uniform transcendental weight three, its functional form resembling the one of the remainder function of the two-loop hexagon Wilson loop in four dimensions.