  We study 1-loop MHV amplitudes in N=4 super Yang-Mills theory and in N=8
supergravity. For Yang-Mills we find that the simple form for the full
amplitude presented by Del Duca, Dixon and Maltoni naturally leads to one that
has physical residues on all compact contours. After expanding the simple form
in terms of standard scalar integrals, we introduce redundancies under certain
symmetry considerations to impose the color-kinematics duality of Bern,
Carrasco and Johansson (BCJ). For five particles we directly find the results
of Carrasco and Johansson as well as a new compact form for the supergravity
amplitude. For six particles we find that all kinematic dual Jacobi identities
are encapsulated in a single functional equation relating the expansion
coefficients. By the BCJ double-copy construction we obtain a formula for the
corresponding N=8 supergravity amplitude. Quite surprisingly, all physical
information becomes independent of the expansion coefficients modulo the
functional equation. In other words, there is no need to solve the functional
equation at all. This is quite welcome as the functional equation we find,
using our restricted set of redundancies, actually has no solutions. For this
reason we call these results virtual color-kinematics duality. We end with
speculations about the meaning of an interesting global vs. local feature of
the functional equation and the situation at higher points.
