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

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...

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Bibliographic Details
Published in:arXiv.org 2022-09
Main Authors: Guo, Yuanhong, Wang, Lei, Yang, Gang
Format: Article
Language:English
Subjects:
Form factors
Mathematical analysis
Operators (mathematics)
Polygons
Statistical methods
Tensors
Online Access:Get full text
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Summary: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. A preliminary study at three loops using symbol bootstrap is discussed.
ISSN:2331-8422