Off-shell minimal form factors

TL;DR

This paper computes two-loop off-shell minimal form factors of half-BPS operators in planar N=4 sYM, revealing their exponentiation, infrared structure, and relation to conformal case symbols using novel massive and superspace techniques.

Contribution

It introduces two complementary methods to construct off-shell form factors in N=4 sYM, including Coulomb branch mass deformation and off-shell superspace algebra, and analyzes their infrared behavior.

Findings

Form factors exponentiate in the near-mass-shell limit.

Confirmed the octagon anomalous dimension as the Sudakov coefficient.

Identified the symbol of the finite remainder matches the conformal case, with different beyond-the-symbol terms.

Abstract

We study off-shell n-particle form factors of half-BPS operators built from n complex scalar fields at the two-loop order in the planar maximally supersymmetric Yang-Mills theory (sYM). These are known as minimal form factors. We construct their representation as a sum of independent scalar Feynman integrals relying on two complementary techniques. First, by going to the Coulomb branch of the theory by employing the spontaneous symmetry breaking which induces masses, but only for external particles while retaining masslessness for virtual states propagating in quantum loops. For a low number of external legs, this entails an uplift of massless integrands to their massive counterparts. Second, utilizing the N=1 superspace formulation of the N=4 sYM and performing algebra of covariant derivatives off-shell. Both techniques provide identical results. These form factors are then studied in the near-mass-shell limit with the off-shellness regularizing emerging infrared divergences. We observe their exponentiation and confirm the octagon anomalous dimension, not the cusp, as the coefficient of the Sudakov double logarithmic behavior. By subtracting these singularities and defining a finite remainder, we verified that its symbol is identical to the one found a decade ago in the conformal case. Beyond-the-symbol contributions are different in the two cases, however.