Off-shell form factor in N=4 sYM at three loops

TL;DR

This paper calculates the off-shell two-particle form factor in N=4 super Yang-Mills theory up to three loops, revealing exponentiation properties and a conjectured all-loop relation to the null octagon, advancing understanding of infrared behavior and integrability.

Contribution

It provides the first detailed three-loop calculation of the off-shell form factor in N=4 sYM and proposes a conjecture linking it to the null octagon at all orders.

Findings

Infrared and finite parts exponentiate up to three loops.

Coefficient of double logarithm determined by octagon anomalous dimension.

Logarithm of the form factor equals twice the null octagon logarithm at this order.

Abstract

In this paper we provide a detailed account of our calculation, briefly reported in arXiv:2209.09263, of a two-particle form factor of the lowest components of the stress-tensor multiplet in N=4 sYM theory on its Coulomb branch, which is interpreted as an off-shell kinematical regime. We demonstrate that up to three-loop order, both its infrared-divergent as well as finite parts do exponentiate in the Sudakov regime, with the coefficient accompanying the double logarithm being determined by the octagon anomalous dimension $\Gamma_{\rm oct}$. We also observe that up to this order in 't Hooft coupling the logarithm of the Sudakov form factor is identical to twice the logarithm of the null octagon, which was introduced within the context of integrability-based computation of four point correlators with infinitely large R-charges. The null octagon is known in a closed form for all values of the 't Hooft coupling constant and kinematical parameters. We conjecture that the relation between the former and the off-shell Sudakov form factor holds to all loop orders.