Amplitudes, Form Factors and the Dilatation Operator in $\mathcal{N}=4$ SYM Theory

Abstract

We study the form factor of a generic gauge-invariant local composite operator in $\mathcal{N}=4$ SYM theory. At tree level and for a minimal number of external on-shell super fields, we find that the form factor precisely yields the spin-chain picture of integrability in the language of scattering amplitudes. Moreover, we compute the cut-constructible part of the one-loop correction to this minimal form factor via generalised unitarity. From its UV divergence, we obtain the complete one-loop dilatation operator of $\mathcal{N}=4$ SYM theory. Thus, we provide a field-theoretic derivation of a relation between the one-loop dilatation operator and the four-point tree-level amplitude which was observed earlier. We also comment on the implications of our findings in the context of integrability.

39 pages, several figures, feynmp; v2: references added, typos corrected; v3: references added, typos corrected, one explanation improved, matches published version

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Cited by in corpus (12)

• Lectures on Yangian Symmetry
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• A note on connected formula for form factors
• Full-color three-loop three-point form factors in N=4 SYM
• Grassmannians and form factors with $q^2=0$ in N=4 SYM theory
• Integrability and unitarity
• Renormalization of effective field theories via on-shell methods: the case of axion-like particles
• Gluonic evanescent operators: classification and one-loop renormalization
• ALPs, the on-shell way
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons