Darboux-Kadomtsev-Petviashvili system as an integrable Chern-Simons multiform theory in infinite dimensional space

The Darboux-Kadomtsev-Petviashvili system is a universal three-dimensional integrable field theory, which is a generating system for the entire Kadomtsev-Petviashvili hierarchy, and at the same time generalizes the Darboux system, describing orthogonal curvilinear coordinates. In this paper, we establish a hierarchy of Lagrangian multiforms for the Darboux-Kadomtsev-Petviashvili system, derived from a hierarchy of Chern-Simons actions in an infinite -dimensional space of Miwa variables. This provides an integrable variational description of this multidimensionally consistent field theory embedded in infinite dimensional space.