Tristan Dennen

Absence of three-loop four-point ultraviolet divergences in N=4 supergravity.

We compute the coefficient of the potential three-loop four-point ultraviolet divergence in pure N=4 supergravity and show that it vanishes, contrary to expectations from symmetry arguments. The recently uncovered duality between color and kinematics is used to greatly streamline the calculation. We comment on all-loop cancellations hinting at further surprises awaiting discovery at higher loops.

Ultraviolet properties of N=4 supergravity at four loops.

We demonstrate that pure N=4 supergravity is ultraviolet divergent at four loops. The form of the divergence suggests that it is due to the rigid U(1) duality-symmetry anomaly of the theory. This is the first known example of an ultraviolet divergence in a pure ungauged supergravity theory in four dimensions. We use the duality between color and kinematics to construct the integrand of the four-loop four-point amplitude, whose ultraviolet divergence is then extracted by standard integration techniques.

Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops

We provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing color factors with specified diagram numerators. Using this, we give explicit forms of ultraviolet divergences at one loop in four, six, and eight dimensions, and at two loops in four dimensions.

Supertwistor space for 6D maximal super Yang-Mills

Abstract6 dimensional maximal super Yang-Mills on-shell amplitudes are formulated in superspace using 6 dimensional spinors. The 3,4,5-point tree amplitudes are obtained by supersymmetrizing their bosonic counterparts and confirmed through the BCFW construction. In contrast to 4 dimensions this superspace is non-chiral, reflecting the fact that one cannot differentiate MHV from

Dual conformal properties of six-dimensional maximal super Yang-Mills amplitudes

\overline {\text{MHV}}

Color dual form for gauge-theory amplitudes.

in 6 dimensions. Combined with unitarity methods, this superspace should be useful for the study of multi-loop D dimensional maximal super Yang-Mills and gravity amplitudes. Furthermore, the non-chiral nature gives a natural framework for an off-shell construction. We show this by matching our result with off-shell D=4 N=4 super Yang-Mills amplitudes, expressed in projective superspace.

Ultraviolet cancellations in half-maximal supergravity as a consequence of the double-copy structure

We demonstrate that the tree-level amplitudes of maximal super-Yang-Mills theory in six dimensions, when stripped of their overall momentum and supermomentum delta functions, are covariant with respect to the six-dimensional dual conformal group. Using the generalized unitarity method, we demonstrate that this property is also present for loop amplitudes. Since the six-dimensional amplitudes can be interpreted as massive four-dimensional ones, this implies that the six-dimensional symmetry is also present in the massively regulated four-dimensional

The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops

\mathcal{N} = 4

γγγγproduction at the LHC: An application of2→4analytic unitarity

super-Yang-Mills amplitudes.

Four photon production at the LHC: an application of 2->4 analytic unitarity

Recently a duality between color and kinematics has been proposed, exposing a new unexpected structure in gauge theory and gravity scattering amplitudes. Here we propose that the relation goes deeper, allowing us to reorganize amplitudes into a form reminiscent of the standard color decomposition in terms of traces over generators, but with the role of color and kinematics swapped. By imposing additional conditions similar to Kleiss-Kuijf relations between partial amplitudes, the relationship between the earlier form satisfying the duality and the current one is invertible. We comment on extensions to loop level.