Emergent gauge symmetry in active Brownian matter

We investigate a two-dimensional system of interacting Active Brownian Particles.Using the Martin-Siggia-Rose-Janssen-de Dominicis formalism, we built up the generating functional for correlation functions.We study in detail the hydrodynamic regime with a constant density stationary state.Our findings reveal that, within a small density fluctuations regime, an emergent U (1) gauge symmetry arises, originated from the conservation of fluid vorticity.Consequently, the interaction between the orientational order parameter and density fluctuations can be cast into a gauge theory, where the concept of "electric charge density" aligns with the local vorticity of the original fluid.We study in detail the case of a microscopic local two-body interaction.We show that, upon integrating out the gauge fields, the stationary states of the rotational degrees of freedom satisfy a non-local Frank free energy for a nematic fluid.We give explicit expressions for the splay and bend elastic constants as a function of the Péclet number (Pe) and the diffusion interaction constant (k d ).