Amplitudes, Form Factors and the Dilatation Operator of N=4 SYM Theory
Abstract:
"Form factors form a bridge between the purely off-shell correlation
functions and the purely on-shell amplitudes. In this talk, 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 fields, the
form factor exactly realises the spin-chain picture of N=4 SYM theory in
the language of scattering amplitudes. Via generalised unitarity, we
obtain the cut-constructible part of the one-loop correction to the
minimal form factor of a generic operator. Its UV divergence yields the
complete one-loop dilatation operator of the theory. Proceeding to the next
loop order, we compute the complete two-loop correction to the two-point
form factor of the Konishi operator via unitarity and obtain the two-loop
Konishi anomalous dimensions from it. For the Konishi operator as well as
other non-protected operators, important subtleties arise which require an
extension of the method of unitarity. The talk is based on the recent
works 1410.6309 and 1410.8485."