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.
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Wilhelm, M. Amplitudes, form factors and the dilatation operator in \( \mathcal{N}=4 \) SYM theory. J. High Energ. Phys. 2015, 149 (2015). https://doi.org/10.1007/JHEP02(2015)149
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DOI: https://doi.org/10.1007/JHEP02(2015)149