Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2014-26

Matthias Wilhelm


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


Abstract: We study the form factor of a generic gauge-invariant local composite operator in
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 cutconstructible 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 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. PACS: 11.15.-q; 11.30.Pb; 11.25.Tq; 11.55.-m
Keywords: Super-Yang-Mills; Form factors; On-shell methods; Anomalous dimensions; Integrability;


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), P-2014-26


39 pp.