  We consider a `color density matrix' in gauge theory. We argue that it
systematically resums large logarithms originating from wide-angle soft
radiation, sometimes referred to as non-global logarithms, to all logarithmic
orders. We calculate its anomalous dimension at leading- and next-to-leading
order. Combined with a conformal transformation known to relate this problem to
shockwave scattering in the Regge limit, this is used to rederive the
next-to-leading order Balitsky-Fadin-Kuraev-Lipatov equation (including its
nonlinear generalization, the so-called Balitsky-JIMWLK equation), finding
perfect agreement with the literature. Exponentiation of divergences to all
logarithmic orders is demonstrated. The possibility of obtaining the evolution
equation (and BFKL) to three-loop is discussed.
