Matrix generalizations of some dynamic field theories Original Research Article

We introduce matrix generalizations of the Navier-Stokes (NS) equation for fluid flow, and the Kardar-Parisi-Zhang (KPZ) equation for interface growth. The underlying field, velocity for the NS equation, or the height in the case of KPZ, is promoted to a matrix that transforms as the adjoint representation of SU (N). Perturbative expansions simplify in the N → ∞ limit, dominated by planar graphs. We provide the results of a one-loop analysis, but have not succeeded in finding the full solution of the theory in this limit.