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

Understand

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.