Konishi Form Factor at Three Loop in $\mathcal{N}=4$ SYM

Abstract

We present the first results on the third order corrections to on-shell form factor (FF) of the Konishi operator in $\mathcal{N}=4$ supersymmetric Yang-Mills theory using Feynman diagrammatic approach in modified dimensional reduction ($\overline{DR}$) scheme. We show that it satisfies KG equation in $\overline{DR}$ scheme while the result obtained in four dimensional helicity (FDH) scheme needs to be suitably modified not only to satisfy the KG equation but also to get the correct ultraviolet (UV) anomalous dimensions. We find that the cusp, soft and collinear anomalous dimensions obtained to third order are same as those of the FF of the half-BPS operator confirming the universality of the infrared (IR) structures of on-shell form factors. In addition, the highest transcendental terms of the FF of Konishi operator are identical to those of half-BPS operator indicating the probable existence of deeper structure of the on-shell FF. We also confirm the UV anomalous dimensions of Konishi operator up to third order providing a consistency check on the both UV and universal IR structures in $\mathcal{N}=4$.

7 pages

References in corpus (14)

• Algorithm FIRE -- Feynman Integral REduction
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Higher-Order threshold effects to inclusive processes in QCD
• Wrapping at four loops in N=4 SYM
• Anomalous dimension with wrapping at four loops in N=4 SYM
• Four-Loop Cusp Anomalous Dimension From Obstructions
• Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• Master Integrals for Fermionic Contributions to Massless Three-Loop Form Factors
• Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
• Pseudo-scalar Form Factors at Three Loops in QCD
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• Spin-2 Form Factors at Three Loop in QCD

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• The Curious Case of Leading Transcendentality: Three Point Form Factors
• An Operator Product Expansion for Form Factors II. Born level
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