Time reparametrization symmetry in a structural glass model

We explore the existence of time reparametrization symmetry in a particle system with quenched disorder. The system's density fluctuations are described by a stochastic equation (D.~S.~Dean,~J.~Phys.~A:Math. Gen \textbf{29}, L613 (1996)). Using the Renormalization Group (RG) on the Martin-Siggia-Rose generating functional, we analytically probe the long time dynamics by systematically integrating over short time scale fluctuations. We find that the RG flow converges to a fixed point that is invariant under reparametrizations of the time variable.