Using the duality between color and kinematics, we construct two-loop four point 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 is an element of and show that it non-trivially cancels out as expected.

We present a new color decomposition for QCD amplitudes at one-loop level as a generalization of the Del Duca-Dixon-Maltoni and Johansson-Ochirov decomposition at tree level. Starting from a minimal basis of planar primitive amplitudes we write down a color decomposition that is free of linear dependencies among appearing primitive amplitudes or color factors. The conjectured decomposition applies to any number of quark flavors and is independent of the choice of gauge group and matter representation. The results also hold for higher-dimensional or supersymmetric extensions of QCD. We provide expressions for any number of external quark-antiquark pairs and gluons. [GRAPHICS] .

We develop an iterative method for constructing four-dimensional generalized unitarity cuts in N = 2 supersymmetric Yang-Mills (SYM) theory coupled to fundamental matter hypermultiplets (N = 2 SQCD). For iterated two-particle cuts, specifically those involving only four-point amplitudes, this implies simple diagrammatic rules for assembling the cuts to any loop order, reminiscent of the rung rule in N = 4 SYM. By identifying physical poles, the construction simplifies the task of extracting complete integrands. In combination with the duality between color and kinematics we construct all four-point massless MHV-sector scattering amplitudes up to two loops in N = 2 SQCD, including those with matter on external legs. Our results reveal chiral infrared-finite integrands closely related to those found using loop-level BCFW recursion. The integrands are valid in D <= 6 dimensions with external states in a four-dimensional subspace; the upper bound is dictated by our use of six-dimensional chiral N = (1, 0) SYM as a means of dimensionally regulating loop integrals.

We present the fully integrated form of the two-loop four-gluon amplitude in N=2 supersymmetric quantum chromodynamics with gauge group SU(Nc) and with Nf massless supersymmetric quarks (hypermultiplets) in the fundamental representation. Our result maintains full dependence on Nc and Nf, and relies on the existence of a compact integrand representation that exhibits the duality between color and kinematics. Specializing to the N=2 superconformal theory, where Nf=2Nc , we obtain remarkably simple amplitudes that have an analytic structure close to that of N=4 super-Yang-Mills theory, except that now certain lower-weight terms appear. We comment on the corresponding results for other gauge groups.