Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons

• Published in: Communications in theoretical physics 2025-01
• Main Authors: Guo, Yuanhong, Wang, Lei, Yang, Gang
• Format: Article
• Language: English
• ISSN: 0253-6102; 1572-9494
• DOI: 10.1088/1572-9494/ada916

We obtain for the first time the analytic two-loop four-point MHV lightlike form factor of the stress-tensor supermultiplet in planar ${\cal N}=4$ SYM where the momentum $q$ carried by the operator is taken to be massless. Remarkably, we find that the two-loop result can be constrained uniquely by the infrared divergences and the collinear limits using the master-bootstrap method. Moreover, the remainder function depends only on three dual conformal invariant variables, which can be understood from a hidden dual conformal symmetry of the form factor arising in the lightlike limit of $q$. The symbol alphabet of the remainder contains only nine letters, which are closed under the action of the dihedral group $D_4$. Based on the dual description in terms of periodic Wilson lines (null-wrapped polygons), we also consider a new OPE picture for the lightlike form factors and introduce a new form factor transition that corresponds to the three-point lightlike form factor. With the form factor results up to two loops, we make some all-loop predictions using the OPE picture.