Two-loop supersymmetric QCD and half-maximal supergravity amplitudes

Author: Henrik Johansson, Gregor Kälin and Gustav Mogull Preprint Number: UUITP-19/17 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=5-2e and show that it non-trivially cancels out as expected.