Graviton and Gluon Scattering from First Principles.

Graviton and gluon scattering are studied from minimal physical assumptions such as Poincare and gauge symmetry as well as unitarity. The assumptions lead to an interesting and surprisingly restrictive set of linear equations. This shows gluon and graviton scattering to be related in many field and string theories, explaining and extending several known results. By systematic analysis exceptional graviton scattering amplitudes are derived, which in general dimensions cannot be related to gluon amplitudes. The simplicity of the formalism guarantees wide further applicability to gauge and gravity theories.

Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory.

The lightlike cusp anomalous dimension is a universal function that controls infrared divergences in quite general gauge theories. In the maximally supersymmetric Yang-Mills theory this function is fixed fully by integrability to the three-loop order. At four loops a nonplanar correction appears which we obtain for the first time from a numerical computation of the Sudakov form factor. Key ingredients are widely applicable methods to control the number-theoretic aspects of the appearing integrals. Our result shows explicitly that quadratic Casimir scaling breaks down at four loops.

Maximal R-symmetry violating amplitudes in type IIb superstring theory.

On-shell superspace techniques are used to quantify R-symmetry violation in type IIB superstring theory amplitudes in a flat background in 10 dimensions. This shows the existence of a particularly simple class of nonvanishing amplitudes in this theory, which violate R symmetry maximally. General properties of the class and some of its extensions are established that at string tree level are shown to determine the first three nontrivial effective field theory contributions to all multiplicity. This leads to a natural conjecture for the exact analytic part of the first two of these.