Critical behavior of active Brownian particles: Connection to field theories

We explore the relation between active Brownian particles, a minimal particle-based model for active matter, and scalar field theories. Both show a liquid-gas-like phase transition toward stable coexistence of a dense liquid with a dilute active gas that terminates in a critical point. However, a comprehensive mapping between the particle-based model parameters and the effective coefficients governing the field theories has not been established yet. We discuss conflicting recent numerical results for the critical exponents of active Brownian particles in two dimensions. Starting from the intermediate effective hydrodynamic equations, we then present a construction for a scalar order parameter for active Brownian particles that yields the active model B+. We argue that a crucial ingredient is the coupling between density and polarization in the particle current. The renormalization flow close to two dimensions exhibits a pair of perturbative fixed points that limit the attractive basin of the Wilson-Fisher fixed point, with the perspective that the critical behavior of active Brownian particles in two dimensions is governed by a strong-coupling fixed point different from Wilson-Fisher and not necessarily corresponding to Ising universality.