title: Harmonic R matrices for scattering amplitudes and spectral regularization.
abstract: Planar N = 4 supersymmetric Yang-Mills theory appears to be integrable. While this allows one to find this theory's exact spectrum, integrability has hitherto been of no direct use for scattering amplitudes. To remedy this, we deform all scattering amplitudes by a spectral parameter. The deformed tree-level four-point function turns out to be essentially the one-loop R matrix of the integrable N = 4 spin chain satisfying the Yang-Baxter equation. Deformed on-shell three-point functions yield novel three-leg R matrices satisfying bootstrap equations. Finally, we supply initial evidence that the spectral parameter might find its use as a novel symmetry-respecting regulator replacing dimensional regularization. Its physical meaning is a local deformation of particle helicity, a fact which might be useful for a much larger class of nonintegrable four-dimensional field theories.
authors.affiliation: Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany.
authors.forename: Livia
authors.initials: L
authors.lastname: Ferro
authors.affiliation: Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin, IRIS Adlershof, Zum Großen Windkanal 6, 12489 Berlin, Germany.
authors.forename: Tomasz
authors.initials: T
authors.lastname: Łukowski
authors.affiliation: Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany and Theory Group, DESY, Notkestraße 85, 22603 Hamburg, Germany.
authors.forename: Carlo
authors.initials: C
authors.lastname: Meneghelli
authors.affiliation: Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany.
authors.forename: Jan
authors.initials: J
authors.lastname: Plefka
authors.affiliation: Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin, IRIS Adlershof, Zum Großen Windkanal 6, 12489 Berlin, Germany and MPI für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Potsdam, Germany.
authors.forename: Matthias
authors.initials: M
authors.lastname: Staudacher