Critical theory of Pomeranchuk transitions via high-dimensional bosonization

Pomeranchuk instability refers to the spontaneous breaking of rotation symmetry in Fermi liquids driven only by Fermi liquid interactions. Using high dimensional bosonization, we show that the fluctuating mode corresponding to the Pomeranchuk transitions in 2D decouples asymptotically from the particle-hole continuum as the Fermi liquid parameter approaches the instability. The resultant theory in terms of this critical mode has dynamical critical exponent z = 2 and only one marginally irrelevant quartic perturbation, akin to the Gaussian fixed point of classical \phi^4 theory in 4 dimensions.