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Journal of High Energy Physics

, 2015:149 | Cite as

Amplitudes, form factors and the dilatation operator in \( \mathcal{N}=4 \) SYM theory

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Regular Article - Theoretical Physics
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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.

Keywords

Scattering Amplitudes Supersymmetric gauge theory AdS-CFT Correspondence Integrable Field Theories 
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© The Author(s) 2015

Authors and Affiliations

  1. 1.Institut für Mathematik und Institut für PhysikHumboldt-Universität zu Berlin, IRIS GebäudeBerlinGermany

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