Configuration space action for high-dimensional bosonization and its instabilities

We study the framework of high dimensional bosonization, specifically in 2D. We find that, the action first obtained in the 90s is actually a phase space action and can be reduced to a configuration space Lagrangian that looks closest to the final form of 1D bosonization. With Landau parameters at hand, we analyze the Pomeranchuk instability (of Fermi surface distortion), and find that that the instability is locally controlled by one real scalar bosonic mode.