On-Shell Methods for the Two-Loop Dilatation Operator and Finite Remainders

Abstract

We compute the two-loop minimal form factors of all operators in the SU(2) sector of planar N=4 SYM theory via on-shell unitarity methods. From the UV divergence of this result, we obtain the two-loop dilatation operator in this sector. Furthermore, we calculate the corresponding finite remainder functions. Since the operators break the supersymmetry, the remainder functions do not have the property of uniform transcendentality. However, the leading transcendentality part turns out to be universal and is identical to the corresponding BPS expressions. The remainder functions are shown to satisfy linear relations which can be explained by Ward identities of form factors following from R-symmetry.

24 pages; v2: typos corrected, some formulations clarified, matches published version

References in corpus (13)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• Form factors at strong coupling via a Y-system
• On the highest transcendentality in N=4 SUSY
• Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
• Exacting N=4 Superconformal Symmetry
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• On form factors in N=4 sym
• The last of the simple remainders
• Amplitudes, Form Factors and the Dilatation Operator in $\mathcal{N}=4$ SYM Theory
• A Twistorial Approach to Integrability in N=4 SYM
• Integrability and MHV diagrams in N=4 supersymmetric Yang-Mills theory
• Integrability and unitarity

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