Monodromies and the structure of gauge and gravity amplitudes

by Pierre Vanhove (IHES & CEA Saclay)

Tuesday 18 May 2010, 14:00 → 15:00 Europe/Zurich

TH Theory Conference Room (CERN)

We show that different color-ordered tree-level amplitudes in gauge theories satisfy monodromy relations. These relations imply the existence of minimal basis of amplitude and provide the numerator factors of the amplitude for a parameterisation of the tree-level amplitude using only cubic vertices. Through the cuts, these tree-level relations give rise to non-trivial identities at loop level. Applications to supergravity amplitudes follow straightforwardly through the KLT-relations. At higher loop this allows to control the critical ultraviolet behaviour of the four-graviton amplitude in N=8 supergravity to all order in perturbation. We argue this implies that the four-graviton N=8 amplitudes has a seven-loop logarithmic divergence in four dimensions.