On perturbative scattering amplitudes in maximally supersymmetric theories

Abstract

There has been substantial calculational progress in the last few years in maximally supersymmetric theories, revealing unexpected simplicity, new structures and symmetries. In this thesis, after reviewing some of the recent advances in N = 4 super Yang-Mills and N = 8 supergravity, we present calculations of perturbative scattering amplitudes and polygonal lightlike Wilson loops that lead to interesting new results. In N = 8 supergravity, we use supersymmetric generalised unitarity to calculate supercoe cients of box functions in the expansion of scattering amplitudes at one loop. Recent advances have presented tree-level amplitudes in N = 8 supergravity in terms of sums of terms containing squares of colour-ordered Yang-Mills superamplitudes. We develop the consequences of these results for the structure of one-loop supercoe cients, recasting them as sums of squares of N = 4 Yang-Mills expressions with certain coe cients inherited from the tree-level superamplitudes. This provides new expressions for all one-loop box coe cients in N = 8 supergravity, which we check against known results in a number of cases. In N = 4 super Yang-Mills, we focus our attention on one of the many remarkable features of MHV scattering amplitudes, their conjectured duality to lightlike polygon Wilson loops, which is expected to hold to all orders in perturbation theory. This duality is usually expressed in terms of purely four-dimensional quantities obtained by appropriate subtraction of the infrared and ultraviolet divergences from amplitudes and Wilson loops respectively. By explicit calculation, we demonstrate the completely unanticipated fact that the equality continues to hold at two loops through O( ) in dimensional regularisation for both the four-particle amplitude and the (parity-even part of the) ve-particle amplitude.