Our results show, for the first time, how to use continuous higher-form symmetries to characterise the dynamical aspects of topological phase transitions. The applications of these results range from plasma phase transition in electromagnetism, QCD phase transition in quark-gluon plasma, superfluid phase transition, superconducting phase transition, solid/liquid phase transition etc. We addressed the potential causality and stability issues in the EFT framework of relativistic hydrodynamics, which are crucial for any practical application of the EFT technology to real world scenarios. Our results also show for the first time how to systematically use approximate symmetries to constraint the dynamics of hydrodynamic systems. Using our results, we were able to derive certain phenomenological constraints on transport coefficients in systems with approximate symmetries that were empirically discovered in the literature using holographic modelling. We also discovered entirely new transport coefficients pertaining to the modification of thermodynamic susceptibilities in the presence of explicit symmetry breaking that were previously overlooked in the literature. We have developed novel field theoretic understanding of fractons by systematically coupling these systems to spacetime backgrounds without boost symmetry. We have developed the requisite technology to apply the non-equilibrium effective field theory technology to real world scenarios where the fluid is confined within a finite box, with far-reaching consequences in various physical systems in condensed-matter physics and biophysics.
