| Summary: | Abstract Using the duality between color and kinematics, we construct two-loop four-point scattering amplitudes in N = 2 $$ \mathcal{N}=2 $$ 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 N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ SYM theory. By exploiting a close connection with N = 4 $$ \mathcal{N}=4 $$ SYM theory — and, equivalently, six-dimensional N = 1 1 $$ \mathcal{N}=\left(1,1\right) $$ 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 N = 1 1 $$ \mathcal{N}=\left(1,1\right) $$ and N = 2 0 $$ \mathcal{N}=\left(2,0\right) $$ 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.
|
|---|