Exact Off Shell Sudakov Form Factor in N=4 Supersymmetric Yang-Mills Theory

We consider the Sudakov form factor in planar N 1/4 4 supersymmetric Yang-Mills theory in the off shell kinematical regime, which can be achieved by considering the theory on its Coulomb branch. We demonstrate that for up to three loops both the infrared-divergent as well as the finite terms do exponentiate, with the coefficient accompanying log2om2 thorn determined by the octagon anomalous dimension Gamma oct. This behavior is in stark contrast to previous conjectural accounts in the literature. Together with the finite terms we observe that for up to three loops the logarithm of the Sudakov form factor is identical to twice the logarithm of the null octagon O0, which was recently introduced within the context of integrability-based approaches to four point correlation functions with infinitely large R charges. The null octagon O0 is known in a closed form for all values of the 't Hooft coupling constant and kinematical parameters. We conjecture that the relation between O0 and the off shell Sudakov form factor will hold to all loop orders.

Automated summary

We study the Sudakov form factor in the off-shell kinematic regime of planar N=4 supersymmetric Yang-Mills theory, which is achieved by considering the theory on its Coulomb branch. We show that both the infrared-divergent and finite terms exponentiate up to three loops, with the coefficient determined by the octagon anomalous dimension. This behavior contradicts previous conjectural accounts. We also find that the logarithm of the Sudakov form factor is equivalent to twice the logarithm of the null octagon O0, which has a closed form expression for all values of the 't Hooft coupling constant and kinematical parameters.