Two-loop supersymmetric QCD and half-maximal supergravity amplitudes

Abstract

Using the duality between color and kinematics, we construct two-loop four-point scattering amplitudes in mathcal{N}=2 super-Yang-Mills (SYM) theory coupled to Nf fundamental hypermultiplets. Our results are valid in D ≤ 6 dimensions, where the upper bound corresponds to six-dimensional chiral mathcal{N}=left(1,0right) SYM theory. By exploiting a close connection with mathcal{N}=4 SYM theory — and, equivalently, six-dimensional mathcal{N}=left(1,1right) 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 Nf 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 mathcal{N}=left(1,1right) and mathcal{N}=left(2,0right) supersymmetry. Finally, we extract the potential ultraviolet divergence of half-maximal supergravity in D = 5 − 2ϵ and show that it non-trivially cancels out as expected.