We study the perturbative expansion of N = 8 supergravity in four dimensions from the viewpoint of the "no-triangle" hypothesis, which states that one-loop graviton amplitudes in N = 8 supergravity only contain scalar box integral functions. Our computations constitute a direct proof at six-points and support the no-triangle conjecture for seven-point amplitudes and beyond.

We obtain a CSW-style formalism for calculating graviton scattering amplitudes and prove its validity through the use of a special type of BCFW-like parameter shift. The procedure is illustrated with explicit examples.

We re-compute the recently derived two-loop five-point all plus Yang-Mills amplitude using Unitarity and Recursion. Recursion requires augmented recursion to determine the sub-leading pole. Using these methods the simplicity of this amplitude is understood.

We characterise the one-loop amplitudes for N = 6 and N = 4 supergravity in four dimensions. For N = 6 we find that the one-loop n-point amplitudes can be expanded in terms of scalar box and triangle functions only. This simplification is consistent with a loop momentum power count of n − 3, which we would interpret as being n + 4 for gravity with a further −7 from the N = 6 superalgebra. For N = 4 we find that the amplitude is consistent with a loop momentum power count of n, which we would interpret as being n + 4 for gravity with a further −4 from the N = 4 superalgebra. Specifically the N = 4 amplitudes contain non-cut-constructible rational terms.

We present an analytic expression for the six-point all-plus helicity amplitude in QCD at two loops. We compute the rational terms in a compact analytic form organized by their singularity structure.