  In prior work the authors introduced a parabolic flow for pluriclosed
metrics, referred to as pluriclosed flow. We also demonstrated that this flow,
after certain gauge transformations, gives a class of solutions to the
renormalization group flow of the nonlinear sigma model with B-field. Using
these transformations, we show that our pluriclosed flow preserves generalized
Kahler structures in a natural way. Equivalently, when coupled with a
nontrivial evolution equation for the two complex structures, the B-field
renormalization group flow also preserves generalized Kahler structure. We
emphasize that it is crucial to evolve the complex structures in the right way
to establish this fact.
