A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field hμν(x) and position $$ {x}_i^{\mu}\left({\tau}_i\right) $$ x i μ τ i of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation 〈hμv(k)〉 and 2PM two-body deflection $$ \Delta {p}_i^{\mu } $$ Δ p i μ from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 → 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT.

Abstract:We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour.

Using the duality between color and kinematics, we construct two-loop fourpoint scattering amplitudes in N = 2 super-Yang-Mills (SYM) theory coupled to N f fundamental hypermultiplets. Our results are valid in D ≤ 6 dimensions, where the upper bound corresponds to six-dimensional chiral N = (1, 0) SYM theory. By exploiting a close connection with N = 4 SYM theory -and, equivalently, six-dimensional N = (1, 1) SYM theory -we find compact integrands with four-dimensional external vectors in both the maximally-helicity-violating (MHV) and all-chiral-vector sectors. Via the double-copy construction corresponding D-dimensional half-maximal supergravity amplitudes with external graviton multiplets are obtained in the MHV and all-chiral sectors. Appropriately tuning N f enables us to consider both pure and matter-coupled supergravity, with arbitrary numbers of vector multiplets in D = 4. As a bonus, we obtain the integrands of the genuinely six-dimensional supergravities with N = (1, 1) and N = (2, 0) supersymmetry. Finally, we extract the potential ultraviolet divergence of half-maximal supergravity in D = 5 − 2 and show that it non-trivially cancels out as expected.