## Amplitudes, Form Factors and the Dilatation Operator in N=4 SYM Theory

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### Documents

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.
Original language English 149 Journal of High Energy Physics (Online) 2014 02 39 1126-6708 https://doi.org/10.1007/JHEP02(2015)149 Published - 2015 Yes

### Research areas

• hep-th, hep-ph

ID: 227489048