# Two-loop supersymmetric QCD and half-maximal supergravity amplitudes

Journal of High Energy Physics, Sep 2017

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 N f fundamental hypermultiplets. Our results are valid in D ≤ 6 dimensions, where the upper bound corresponds to six-dimensional chiral $\mathcal{N}=\left(1,0\right)$ SYM theory. By exploiting a close connection with $\mathcal{N}=4$ SYM theory — and, equivalently, six-dimensional $\mathcal{N}=\left(1,1\right)$ 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 $\mathcal{N}=\left(1,1\right)$ and $\mathcal{N}=\left(2,0\right)$ 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.

This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2FJHEP09%282017%29019.pdf

Henrik Johansson, Gregor Kälin, Gustav Mogull. Two-loop supersymmetric QCD and half-maximal supergravity amplitudes, Journal of High Energy Physics, 2017, 19, DOI: 10.1007/JHEP09(2017)019